Relevant bibliographies by topics / $K$-theory and operator algebras {Selfadjoint operator algebras}

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic '$K$-theory and operator algebras {Selfadjoint operator algebras}'

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Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "$K$-theory and operator algebras {Selfadjoint operator algebras}"

1

Saito, Kichi-Suke. "Generalized interpolation in finite maximal subdiagonal algebras." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 1 (January 1995): 11–20. http://dx.doi.org/10.1017/s0305004100072893.

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Non-selfadjoint operator algebras have been studied since the paper of Kadison and Singer in 1960. In [1], Arveson introduced the notion of subdiagonal algebras as the generalization of weak *-Dirichlet algebras and studied the analyticity of operator algebras. After that, we have many papers about non-selfadjoint algebras in this direction: nest algebras, CSL algebras, reflexive algebras, analytic operator algebras, analytic crossed products and so on. Since the notion of subdiagonal algebras is the analogue of weak *-Dirichlet algebras, subdiagonal algebras have many fruitful properties from the theory of function algebras. Thus, we have several attempts in this direction: Beurling–Lax–Halmos theorem for invariant subspaces, maximality, factorization theorem and so on.
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Anjidani, Ehsan, and Mohammad Reza Changalvaiy. "Reverse Jensen-Mercer Type Operator Inequalities." Electronic Journal of Linear Algebra 31 (February 5, 2016): 87–99. http://dx.doi.org/10.13001/1081-3810.3058.

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Let $A$ be a selfadjoint operator on a Hilbert space $\mathcal{H}$ with spectrum in an interval $[a,b]$ and $\phi:B(\mathcal{H})\rightarrow B(\mathcal{K})$ be a unital positive linear map, where $\mathcal{K}$ is also a Hilbert space. Let $m,M\in J$ with $m
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Kaad, J., R. Nest, and A. Rennie. "KK-Theory and Spectral Flow in von Neumann Algebras." Journal of K-Theory 10, no. 2 (April 4, 2012): 241–77. http://dx.doi.org/10.1017/is012003003jkt185.

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AbstractWe present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko(J).Given a semifinite spectral triple (A, H, D) relative to (N, τ) with A separable, we construct a class [D] ∈ KK1(A, K(N)). For a unitary u ∈ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u]A[D], and is simply related to the numerical spectral flow, and a refined C*-spectral flow.
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Lance, Christopher. "Book Review: $K$-theory for operator algebras." Bulletin of the American Mathematical Society 18, no. 1 (January 1, 1988): 67–74. http://dx.doi.org/10.1090/s0273-0979-1988-15604-2.

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Dong, Chongying, Kefeng Liu, Xiaonan Ma, and Jian Zhou. "$K$-theory associated to vertex operator algebras." Mathematical Research Letters 11, no. 5 (2004): 629–47. http://dx.doi.org/10.4310/mrl.2004.v11.n5.a7.

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Rosenberg, Jonathan. "The Algebraic K-Theory of Operator Algebras." K-Theory 12, no. 1 (July 1997): 75–99. http://dx.doi.org/10.1023/a:1007736420938.

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Inassaridze, Hvedri, and Tamaz Kandelaki. "K-Theory of Stable Generalized Operator Algebras." K-Theory 27, no. 2 (October 2002): 103–10. http://dx.doi.org/10.1023/a:1021197520756.

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Hebestreit, Fabian, and Steffen Sagave. "Homotopical and operator algebraic twisted K-theory." Mathematische Annalen 378, no. 3-4 (August 15, 2020): 1021–59. http://dx.doi.org/10.1007/s00208-020-02066-6.

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Abstract Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of $$C^*$$ C ∗ -algebras to include multiplicative structures. Our results can also be interpreted in the $$\infty $$ ∞ -categorical setup for parametrized spectra.
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Oyono-Oyono, Hervé, and Guoliang Yu. "Quantitative K-theory and the Künneth formula for operator algebras." Journal of Functional Analysis 277, no. 7 (October 2019): 2003–91. http://dx.doi.org/10.1016/j.jfa.2019.01.009.

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Wright, J. D. M. "K-THEORY FOR OPERATOR ALGEBRAS: (Mathematical Sciences Research Institute Publications 5)." Bulletin of the London Mathematical Society 22, no. 3 (May 1990): 307–8. http://dx.doi.org/10.1112/blms/22.3.307.

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Dissertations / Theses on the topic "$K$-theory and operator algebras {Selfadjoint operator algebras}"

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Flournoy, Cecil Buford Jr. "N-parameter Fibonacci AF C*-Algebras." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1221.

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An n-parameter Fibonacci AF-algebra is determined by a constant incidence matrix K of a special form. The form of the matrix K is defined by a given n-parameter Fibonacci sequence. We compute the K-theory of certain Fibonacci AF-algebra, and relate their K-theory to the K-theory of an AF-algebra defined by incidence matrices that are the transpose of K.
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Starling, Charles B. "Actions of Finite Groups on Substitution Tilings and Their Associated C*-algebras." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/20663.

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The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*-algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*-algebras respectively. Of particular interest are the crossed product C*-algebras; we derive important structure results about them and compute their K-theory.
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de, Silva Nadish. "Contextuality and noncommutative geometry in quantum mechanics." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:1ca8995d-b562-426a-ab89-afab3a18dda2.

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It is argued that the geometric dual of a noncommutative operator algebra represents a notion of quantum state space which differs from existing notions by representing observables as maps from states to outcomes rather than from states to distributions on outcomes. A program of solving for an explicitly geometric manifestation of quantum state space by adapting the spectral presheaf, a construction meant to analyze contextuality in quantum mechanics, to derive simple reconstructions of noncommutative topological tools from their topological prototypes is presented. We associate to each unital C*-algebra A a geometric object--a diagram of topological spaces representing quotient spaces of the noncommutative space underlying A—meant to serve the role of a generalized Gel'fand spectrum. After showing that any functor F from compact Hausdorff spaces to a suitable target category C can be applied directly to these geometric objects to automatically yield an extension F∼ which acts on all unital C*-algebras, we compare a novel formulation of the operator K0 functor to the extension K∼ of the topological K-functor. We then conjecture that the extension of the functor assigning a topological space its topological lattice assigns a unital C*-algebra the topological lattice of its primary ideal spectrum and prove the von Neumann algebraic analogue of this conjecture.
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Pennig, Ulrich. "Twisted K-theory with coefficients in a C*-algebra and obstructions against positive scalar curvature metrics." Doctoral thesis, 2009. http://hdl.handle.net/11858/00-1735-0000-0006-B3D2-7.

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(9183335), Jacob R. Desmond. "Quasidiagonal Extensions of C*-algebras and Obstructions in K-theory." Thesis, 2020.

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Quasidiagonality is a matricial approximation property which asymptotically captures the multiplicative structure of C* -algebras. Quasidiagonal C* -algebras must be stably finite. It has been conjectured by Blackadar and Kirchberg that stably finiteness implies quasidiagonality for the class of separable nuclear C* -algebras. It has also been conjectured that separable exact quasidiagonal C* -algebras are AF embeddable. In this thesis, we study the behavior of these conjectures in the context of extensions 0 → I → E → B → 0. Specifically, we show that if I is exact and connective and B is separable, nuclear, and quasidiagonal (AF embeddable), then E is quasidiagonal (AF embeddable). Additionally, we show that if I is of the form C(X) ⊗ K for a compact metrizable space X and B is separable, nuclear, quasidiagonal (AF embeddable), and satisfies the UCT, then E is quasidiagonal (AF embeddable) if and only if E is stably finite.
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Francis, Michael. "Traces, one-parameter flows and K-theory." Thesis, 2014. http://hdl.handle.net/1828/5649.

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Given a C*-algebra $A$ endowed with an action $\alpha$ of $\R$ and an $\alpha$-invariant trace $\tau$, there is a canonical dual trace $\widehat \tau$ on the crossed product $A \rtimes_\alpha \R$. This dual trace induces (as would any suitable trace) a real-valued homomorphism $\widehat \tau_* : K_0(A \rtimes_\alpha \R) \to \R$ on the even $K$-theory group. Recall there is a natural isomorphism $\phi_\alpha^i : K_i(A) \to K_{i+1}(A \rtimes_\alpha \R)$, the Connes-Thom isomorphism. The attraction of describing $\widehat \tau_* \circ \phi_\alpha^1$ directly in terms of the generators of $K_1(A)$ is clear. Indeed, the paper where the isomorphisms $\{\phi_\alpha^0,\phi_\alpha^1\}$ first appear sees Connes show that $\widehat \tau_* \phi_\alpha^1[u] = \frac{1}{2 \pi i} \tau(\delta(u) u^*)$, where $\delta = \frac{d}{dt} \big|_{t=0} \alpha_t(\cdot)$ and $u$ is any appropriate unitary. A careful proof of the aforementioned result occupies a central place in this thesis. To place the result in its proper context, the right-hand side is first considered in its own right, i.e., in isolation from mention of the crossed-product. A study of 1-parameter dynamical systems and exterior equivalence is undertaken, with several useful technical results being proven. A connection is drawn between a lemma of Connes on exterior equivalence and projections, and a quantum-mechanical theorem of Bargmann-Wigner. An introduction to the Connes-Thom isomorphism is supplied and, in the course of this introduction, a refined version of suspension isomorphism $K_1(A) \to K_0(\susp A)$ is formulated and proven. Finally, we embark on a survey of unbounded traces on C*-algebras; when traces are allowed to be unbounded, there is inevitably a certain amount of hard, technical work needed to resolve various domain issues and justify various manipulations.
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Hudson, Daniel. "K-theory correspondences and the Fourier-Mukai transform." Thesis, 2019. http://hdl.handle.net/1828/10837.

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The goal of this thesis is to give an introduction to the geometric picture of bivariant K-theory developed by Emerson and Meyer building on the ideas Connes and Skandalis, and then to apply this machinery to give a geometric proof of a result of Emerson. We begin by giving an overview of topological K-theory, necessary for developing bivariant K-theory. Then we discuss Kasparov's analytic bivariant K-theory, and from there develop topological bivariant K-theory. In the final chapter we state and prove the result of Emerson.
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Schneider, Ansgar. "Die lokale Struktur von T-Dualitätstripeln." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B39F-C.

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Books on the topic "$K$-theory and operator algebras {Selfadjoint operator algebras}"

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Doran, Robert S., Richard V. Kadison, and Efton Park. Operator algebras and their applications: A tribute to Richard V. Kadison : AMS Special Session, Janaury 10-11, 2015, San Antonio, Texas. Providence, Rhode Island: American Mathematical Society, 2016.

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Doran, Robert S., ed. Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/conm/120.

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K-theory for operator algebras. 2nd ed. Cambridge, UK: Cambridge University Press, 1998.

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Blackadar, Bruce. K-Theory for Operator Algebras. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-9572-0.

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K-theory for operator algebras. New York: Springer-Verlag, 1986.

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Argentina) Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry (3rd 2010 Buenos Aires. Topics in noncommutative geometry: Third Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26-August 6, 2010. Edited by Cortiñas, Guillermo, editor of compilation. Providence, RI: American Mathematical Society, 2012.

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NSF/CBMS Regional Conference on Coordinates in Operator Algebras: Groupoids and Categories, Their Representations and Applications (1990 Texas Christian University). Selfadjoint and nonselfadjoint operator algebras and operator theory: Proceedings of the CBMS regional conference held May 19-26, 1990 at Texas Christian University, Fort Worth, Texas with support from the National Science Foundation. Edited by Doran Robert 1937-, National Science Foundation (U.S.), and Conference Board of the Mathematical Sciences. Providence, R.I: American Mathematical Society, 1991.

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Steven, Rosenberg, and Clara L. Aldana. Analysis, geometry, and quantum field theory: International conference in honor of Steve Rosenberg's 60th birthday, September 26-30, 2011, Potsdam University, Potsdam, Germany. Providence, Rhode Island: American Mathematical Society, 2012.

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Rørdam, M. Classification of nuclear C-algebras; entropy in operator algebras. Berlin: Springer, 2002.

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Simon, Barry. Operator theory. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "$K$-theory and operator algebras {Selfadjoint operator algebras}"

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Blackadar, Bruce. "K-Theory and Finiteness." In Operator Algebras, 395–477. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/3-540-28517-2_5.

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Evans, David E. "Twisted K-Theory and Modular Invariants: I Quantum Doubles of Finite Groups." In Operator Algebras, 117–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-34197-0_6.

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Vinod Kumar, P., and M. S. Balasubramani. "On k-Minimal and k-Maximal Operator Space Structures." In Semigroups, Algebras and Operator Theory, 205–15. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2488-4_16.

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Yu, Guoliang. "Quantitative K-theory for geometric operator algebras." In K-Theory for Group C*-Algebras and Semigroup C*-Algebras, 149–65. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59915-1_4.

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Mesland, Bram, Mehmet Haluk Şengün, and Hang Wang. "A K-Theoretic Selberg Trace Formula." In Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology, 403–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43380-2_19.

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Yang, Liming. "Reproducing Kernel of the Space R t(K, μ)." In Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology, 521–34. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43380-2_26.

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Baum, P., and A. Connes. "K-theory for discrete groups." In Operator Algebras and Applications, 1–20. Cambridge University Press, 1989. http://dx.doi.org/10.1017/cbo9780511662270.003.

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Katsoulis, E. G. "Non-selfadjoint operator algebras: dynamics, classification and C*-envelopes." In Recent Advances in Operator Theory and Operator Algebras, 27–82. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315116938-2.

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Murphy, Gerard J. "K-Theory of C*-Algebras." In C*–Algebras and Operator Theory, 217–65. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-08-092496-0.50011-9.

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"C*-algebraic K-theory made concrete, or trick or treat with 2×2 matrix algebras." In Lectures on Operator Theory, 71–76. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/fim/013/10.

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