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Academic literature on the topic 'Invariant subspaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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Journal articles on the topic "Invariant subspaces"

1

IZUCHI, KEI JI, KOU HEI IZUCHI, and YUKO IZUCHI. "SPLITTING INVARIANT SUBSPACES IN THE HARDY SPACE OVER THE BIDISK." Journal of the Australian Mathematical Society 102, no. 2 (May 12, 2016): 205–23. http://dx.doi.org/10.1017/s1446788716000203.

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Let $H^{2}$ be the Hardy space over the bidisk. It is known that Hilbert–Schmidt invariant subspaces of $H^{2}$ have nice properties. An invariant subspace which is unitarily equivalent to some invariant subspace whose continuous spectrum does not coincide with $\overline{\mathbb{D}}$ is Hilbert–Schmidt. We shall introduce the concept of splittingness for invariant subspaces and prove that they are Hilbert–Schmidt.

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Wang, Guo-Hua, Jia-Fu Pang, Yong-Yang Jin, and Bo Ren. "Invariant Subspaces of Short Pulse-Type Equations and Reductions." Symmetry 16, no. 6 (June 18, 2024): 760. http://dx.doi.org/10.3390/sym16060760.

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In this paper, we extend the invariant subspace method to a class of short pulse-type equations. Complete classification results with invariant subspaces from 2 to 5 dimensions are provided. The key step is to take subspaces of solutions of linear ordinary differential equations as invariant subspaces that nonlinear operators admit. Some concrete examples and corresponding reduced systems are presented to illustrate this method.

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ASSADI, AMANOLLAH, MOHAMAD ALI FARZANEH, and HAJI MOHAMMAD MOHAMMADINEJAD. "ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES." Bulletin of the Australian Mathematical Society 99, no. 2 (January 4, 2019): 274–83. http://dx.doi.org/10.1017/s0004972718001363.

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We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.

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Bose, Snehasish, P. Muthukumar, and Jaydeb Sarkar. "Beurling type invariant subspaces of composition operators." Journal of Operator Theory 86, no. 2 (November 15, 2021): 425–38. http://dx.doi.org/10.7900/jot.2020may15.2286.

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The aim of this paper is to answer the following question concerning invariant subspaces of composition operators: characterize φ, holomorphic self maps of D, and inner functions θ∈H∞(D) such that the Beurling type invariant subspace θH2 is an invariant subspace for Cφ. We prove the following result: Cφ(θH2)⊆θH2 if and only if θ∘φθ∈S(D). This classification also allows us to recover or improve some known results on Beurling type invariant subspaces of composition operators.

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Liu, Junfeng. "On Invariant Subspaces for the Shift Operator." Symmetry 11, no. 6 (June 1, 2019): 743. http://dx.doi.org/10.3390/sym11060743.

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In this paper, we improve two known invariant subspace theorems. More specifically, we show that a closed linear subspace M in the Hardy space H p ( D ) ( 1 ≤ p < ∞ ) is invariant under the shift operator M z on H p ( D ) if and only if it is hyperinvariant under M z , and that a closed linear subspace M in the Lebesgue space L 2 ( ∂ D ) is reducing under the shift operator M e i θ on L 2 ( ∂ D ) if and only if it is hyperinvariant under M e i θ . At the same time, we show that there are two large classes of invariant subspaces for M e i θ that are not hyperinvariant subspaces for M e i θ and are also not reducing subspaces for M e i θ . Moreover, we still show that there is a large class of hyperinvariant subspaces for M z that are not reducing subspaces for M z . Furthermore, we gave two new versions of the formula of the reproducing function in the Hardy space H 2 ( D ) , which are the analogue of the formula of the reproducing function in the Bergman space A 2 ( D ) . In addition, the conclusions in this paper are interesting now, or later if they are written into the literature of invariant subspaces and function spaces.

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Krivosheev, A. S., and O. A. Krivosheeva. "Invariant Subspaces in Unbounded Domains." Issues of Analysis 28, no. 3 (November 2021): 91–107. http://dx.doi.org/10.15393/j3.art.2021.10870.

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Szekelyhidi, Laszlo, and Seyyed Mohammad Tabatabaie. "Invariant Subspaces on KPC-Hypergroups." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 1 (March 25, 2019): 122–30. http://dx.doi.org/10.15407/mag15.01.122.

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Forouzanfar, AM, S. Khorshidvandpour, and Z. Bahmani. "Uniformly invariant normed spaces." BIBECHANA 10 (October 31, 2013): 31–33. http://dx.doi.org/10.3126/bibechana.v10i0.7555.

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In this work, we introduce the concepts of compactly invariant and uniformly invariant. Also we define sometimes C-invariant closed subspaces and then prove every m-dimensional normed space with m > 1 has a nontrivial sometimes C-invariant closed subspace. Sequentially C-invariant closed subspaces are also introduced. Next, An open problem on the connection between compactly invariant and uniformly invariant normed spaces has been posed. Finally, we prove a theorem on the existence of a positive operator on a strict uniformly invariant Hilbert space. DOI: http://dx.doi.org/10.3126/bibechana.v10i0.7555 BIBECHANA 10 (2014) 31-33

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Fernández-Morales, H. R., A. G. García, M. A. Hernández-Medina, and M. J. Muñoz-Bouzo. "Generalized sampling: From shift-invariant to U-invariant spaces." Analysis and Applications 13, no. 03 (March 5, 2015): 303–29. http://dx.doi.org/10.1142/s0219530514500213.

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The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U.

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Guo, Kunyu, and Dechao Zheng. "Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators." Journal of Functional Analysis 187, no. 2 (December 2001): 308–42. http://dx.doi.org/10.1006/jfan.2001.3820.

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Dissertations / Theses on the topic "Invariant subspaces"

1

Adams, Lynn I. "Classifying Triply-Invariant Subspaces." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121.

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Mahvidi, Ali. "Invariant subspaces of composition operators." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/NQ45739.pdf.

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POSTERNAK, REGINA. "INVARIANT SUBSPACES FOR HIPONORMAL OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2002. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3338@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
O problema do subespaço invariante consiste na seguinte pergunta: será que todo operador (i.e., transformação linear limitada) atuando em um espaço de Hilbert separável (complexo de dimensão infinita) tem subespaço invariante nãotrivial? Este é, possivelmente, o mais importante problema em aberto na teoria de operadores. Em particular, o problema do subespaço invariante permanece em aberto (pelo menos até a presente data) para operadores hiponormais, ou seja, ainda não se sabe se todo operador hiponormal (atuando em um espaço de Hilbert complexo separável) tem subespaço invariante não-trivial. O objetivo desta dissertação é apresentar, de maneira unificada, um levantamento sobre subespaços invariantes para operadores hiponormais. Inicialmente, o problema do subespaço invariante é abordado em sua forma geral (sem restrição a classes de operadores) onde diversos resultados clássicos são expostos. Em seguida, o problema específico de se encontrar subespaços invariantes para operadores hiponormais é apresentado de maneira sistemática. Em particular, investigamos propriedades do espectro de um operador hiponormal que não tenha subespaço invariante não trivial.
The invariant subspace problem is: does every operator acting on an infinite-dimensional complex separable Hilbert space have a nontrivial invariant subspace? This is, probably, the most important open question in the operator theory. In particular, the problem of the invariant subspace remains open (at least until now) for hyponormal operators, that is, it is still unknown whether every hyponormal operator (on a complex separable Hilbert space) has a nontrivial invariant subspace. The purpose of these dissertation is to present, in an unified way, a survey on invariant subspaces for hyponormal operators. At first, the invariant subspace problem is posed in a general form (without any restriction on the operator classes), where some of classical results are discussed. Secondly, the specific problem of finding invariant subspaces for hyponormal operators is presented in a systematic way and, in particular, we show some characteristics of the spectrum of a hyponormal operator with no nontrivial invariant subspace.

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Mehrmann, Volker, and Hongguo Xu. "Lagrangian invariant subspaces of Hamiltonian matrices." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501133.

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The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.

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Wojtasinski, Justyna Agata. "Classifying Triply-Invariant Subspaces for p=3." Akron, OH : University of Akron, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1209134757.

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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2008.
"May, 2008." Title from electronic thesis title page (viewed 07/12/2008) Advisor, Jeffrey M. Riedl; Faculty Readers, Ethel Wheland, Stuart Clay; Department Chair, Joseph Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

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Smith, Rachael Caroline. "Spectral densities and invariant subspaces of operators." Thesis, University of Leeds, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432300.

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Schulze, Bert-Wolfgang, Anton Savin, and Boris Sternin. "Elliptic operators in subspaces and the eta invariant." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2549/.

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The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.

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Lücking, Simon [Verfasser]. "The Daugavet Property and Translation-Invariant Subspaces / Simon Lücking." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1054163154/34.

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9

Jiang, Jiaosheng. "Bounded operators without invariant subspaces on certain Banach spaces." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3037506.

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Hayakawa, Yoshikazu, and D. ŠILJAK Dragoslav. "On almost invariant subspaces of structural systems and decentralized control." IEEE, 1988. http://hdl.handle.net/2237/6854.

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Books on the topic "Invariant subspaces"

1

Radjavi, Heydar. Invariant subspaces. 2nd ed. Mineola, N.Y: Dover Publications, 2003.

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Henry, Helson, Yadav B. S. 1931-, Singh Udita Narayana 1917-1989, University of Delhi. Dept. of Mathematics., and International Conference on "Invariant Subspaces and Allied Topics" (1986 : Dept. of Mathematics, University of Delhi), eds. Invariant subspaces and allied topics. New Delhi: Narosa Pub. House, 1990.

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Mashreghi, Javad, Emmanuel Fricain, and William Ross, eds. Invariant Subspaces of the Shift Operator. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/conm/638.

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1929-, Lancaster Peter, and Rodman L, eds. Invariant subspaces of matrices with applications. New York: Wiley, 1986.

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5

MacDonald, Gordon Wilson. Invariant subspaces for weighted translation operators. Toronto: [s.n.], 1989.

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Chalendar, Isabelle. Modern approaches to the invariant-subspace problem. Cambridge, UK: Cambridge University Press, 2011.

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7

Demmel, James Weldon. Three methods for refining estimates of invariant subspaces. New York: Courant Institute of Mathematical Sciences, New York University, 1985.

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Douglas, R. G., C. M. Pearcy, B. Sz.-Nagy, F. H. Vasilescu, Dan Voiculescu, and Gr Arsene, eds. Advances in Invariant Subspaces and Other Results of Operator Theory. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-7698-8.

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Ciprian, Foiaş, Pearcy Carl M. 1935-, and Conference Board of the Mathematical Sciences., eds. Dual algebras with applications to invariant subspaces and dilation theory. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1985.

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Mashreghi, Javad, Emmanuel Fricain, and William T. Ross. Invariant subspaces of the shift operator: CRM Workshop, Invariant Subspaces of the Shift Operator, August 26-30, 2013, Centre de Recherches Mathematiques, Universite' de Montreal, Montreal. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "Invariant subspaces"

1

Hedenmalm, Haakan, Boris Korenblum, and Kehe Zhu. "Invariant Subspaces." In Graduate Texts in Mathematics, 176–89. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0497-8_6.

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Nikol’skiĭ, Nikolaĭ K. "Invariant Subspaces." In Grundlehren der mathematischen Wissenschaften, 10–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-70151-1_2.

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Kubrusly, Carlos S. "Invariant Subspaces." In Hilbert Space Operators, 1–11. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_1.

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Farenick, Douglas R. "Invariant Subspaces." In Universitext, 77–116. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0097-7_3.

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Katznelson, Yitzhak, and Yonatan Katznelson. "Invariant subspaces." In The Student Mathematical Library, 85–101. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/stml/044/05.

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Abramovich, Y., and C. Aliprantis. "Invariant subspaces." In Graduate Studies in Mathematics, 381–454. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/050/10.

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Abramovich, Y., and C. Aliprantis. "Invariant subspaces." In Problems in Operator Theory, 299–334. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/051/10.

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Duren, Peter, and Alexander Schuster. "Invariant subspaces." In Bergman Spaces, 245–69. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/09.

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Mandrekar, Vidyadhar S., and David A. Redett. "Invariant Subspaces." In Weakly Stationary Random Fields, Invariant Subspaces and Applications, 109–33. Boca Raton: CRC Press, 2018.: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9780203709733-3.

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Trentelman, Harry L., Anton A. Stoorvogel, and Malo Hautus. "Controlled invariant subspaces." In Communications and Control Engineering, 75–106. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0339-4_4.

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Conference papers on the topic "Invariant subspaces"

1

Lemmon, Michael. "Inductive Inference of Invariant Subspaces." In 1993 American Control Conference. IEEE, 1993. http://dx.doi.org/10.23919/acc.1993.4793062.

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Haseli, Masih, and Jorge Cortes. "Fast Identification of Koopman-Invariant Subspaces: Parallel Symmetric Subspace Decomposition." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147223.

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Bajcinca, Naim. "On pole placement and invariant subspaces." In 2013 XXIV International Conference on Information, Communication and Automation Technologies (ICAT). IEEE, 2013. http://dx.doi.org/10.1109/icat.2013.6684081.

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FACCHI, P., V. L. LEPORE, and S. PASCAZIO. "INVARIANT SUBSPACES AND CONTROL OF DECOHERENCE." In Quantum Information and Computing. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774491_0008.

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Aguilera, Alejandra, Carlos Cabrelli, Diana Carbajal, and Victoria Paternostro. "Frames by Iterations and Invariant Subspaces." In 2023 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2023. http://dx.doi.org/10.1109/sampta59647.2023.10301371.

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Li, Na, and Man-Wai Mak. "SNR-invariant PLDA with multiple speaker subspaces." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472742.

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Hogan, Jeffrey A., and Joseph D. Lakey. "Sampling for shift-invariant and wavelet subspaces." In International Symposium on Optical Science and Technology, edited by Akram Aldroubi, Andrew F. Laine, and Michael A. Unser. SPIE, 2000. http://dx.doi.org/10.1117/12.408622.

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Lawrence, Douglas A. "Controlled invariant subspaces for linear impulsive systems." In 2014 American Control Conference - ACC 2014. IEEE, 2014. http://dx.doi.org/10.1109/acc.2014.6858804.

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Lawrence, Douglas A. "Conditioned invariant subspaces for linear impulsive systems." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7172093.

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Otsuka, N. "Generalized invariant subspaces for linear multivariable systems." In UKACC International Conference on Control (CONTROL '98). IEE, 1998. http://dx.doi.org/10.1049/cp:19980461.

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Reports on the topic "Invariant subspaces"

1

Dongarra, J. J., S. Hammarling, and J. H. Wilkinson. Numerical considerations in computing invariant subspaces. Office of Scientific and Technical Information (OSTI), November 1990. http://dx.doi.org/10.2172/6427540.

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Berner, Chad. Shift-invariant subspaces of locally compact abelian groups. Ames (Iowa): Iowa State University, January 2021. http://dx.doi.org/10.31274/cc-20240624-1284.

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Ron, Amos, and Zuowei Shen. Frames and Stable Bases for Shift-Invariant Subspaces of L2(IRd). Fort Belvoir, VA: Defense Technical Information Center, February 1994. http://dx.doi.org/10.21236/ada276470.

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DE Boor, Carl, Ronald A. DeVore, and Amos Ron. Approximation from Shift-Invariant Subspaces of L sup 2 (R sup d). Fort Belvoir, VA: Defense Technical Information Center, July 1991. http://dx.doi.org/10.21236/ada238165.

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