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Academic literature on the topic 'Hyponormal operator'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Hyponormal operator"

1

Chō, Muneo. "Spectral properties of p-hyponormal operators." Glasgow Mathematical Journal 36, no. 1 (1994): 117–22. http://dx.doi.org/10.1017/s0017089500030627.

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Let ℋ be a complex Hilbert space and B(ℋ) be the algebra of all bounded linear opeators on ℋ. An operator T ∈ B(ℋ) is said to be p-hyponormal if (T*T)p–(TT*)p. If p = 1, T is hyponormal and if p = ½ is semi-hyponormal. It is well known that a p-hyponormal operator is p-hyponormal for q≤p. Hyponormal operators have been studied by many authors. The semi-hyponormal operator was first introduced by D. Xia in [7]. The p-hyponormal operators have been studied by A. Aluthge in [1]. Let T be a p-hyponormal operator and T=U|T| be a polar decomposition of T. If U is unitary, Aluthge in [1] proved the f

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2

Chō, Muneo, Dijana Mosic, Biljana Nacevska-Nastovska, and Taiga Saito. "Spectral properties of square hyponormal operators." Filomat 33, no. 15 (2019): 4845–54. http://dx.doi.org/10.2298/fil1915845c.

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In this paper, we introduce a square hyponormal operator as a bounded linear operator T on a complex Hilbert space H such that T2 is a hyponormal operator, and we investigate some basic properties of this operator. Under the hypothesis ?(T) ? (-?(T)) ? {0}, we study spectral properties of a square hyponormal operator. In particular, we show that if z and w are distinct eigen-values of T and x,y ? H are corresponding eigen-vectors, respectively, then ?x,y? = 0. Also, we define nth hyponormal operators and present some properties of this kind of operators.

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3

Gunawan, Gunawan, and Erni Widiyastuti. "KARAKTERISTIK OPERATOR PARANORMAL- * QUASI." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 3, no. 1 (2022): 256–73. http://dx.doi.org/10.46306/lb.v3i1.114.

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Given Hilbert space H over the fields of . This study aimed to investigate the paranormal- * quasi operators and their properties in Hilbert space. The study resulted the properties of paranormal- * quasi operators, hyponormal operator, class A operator, Class A- * operator, p- hyponormal operator for p > 0, - paranormal operators, compact operator, and the relationship between them

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4

Journal, Baghdad Science. "Quasi-posinormal operators." Baghdad Science Journal 7, no. 3 (2010): 1282–87. http://dx.doi.org/10.21123/bsj.7.3.1282-1287.

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In this paper, we introduce a class of operators on a Hilbert space namely quasi-posinormal operators that contain properly the classes of normal operator, hyponormal operators, M–hyponormal operators, dominant operators and posinormal operators . We study some basic properties of these operators .Also we are looking at the relationship between invertibility operator and quasi-posinormal operator .

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5

Duggal, B. P. "On the spectrum of n-tuples of p-hyponormal operators." Glasgow Mathematical Journal 40, no. 1 (1998): 123–31. http://dx.doi.org/10.1017/s0017089500032419.

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Let B(H) denote the algebra of operators (i.e., bounded linear transformations) on the Hilbert space H. A ∈ B (H) is said to be p-hyponormal (0<p<l), if (AA*)γ < (A*A)p. (Of course, a l-hyponormal operator is hyponormal.) The p-hyponormal property is monotonic decreasing in p and a p-hyponormal operator is q-hyponormal operator for all 0<q <p. Let A have the polar decomposition A = U |A|, where U is a partial isometry and |A| denotes the (unique) positive square root of A*A.If A has equal defect and nullity, then the partial isometry U may be taken to be unitary. Let ℋU(p) denot

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6

Han, Young, and Hee Son. "On quasi-M-hyponormal operators." Filomat 25, no. 1 (2011): 37–52. http://dx.doi.org/10.2298/fil1101037h.

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An operator T is called quasi-M -hyponormal if there exists a positive real number M such that T ? (M 2 (T ??)? (T ??))T ? T ? (T ??)(T ??)? T for all ? ? C, which is a generalization of M -hyponormality. In this paper, we consider the local spectral properties for quasi-M -hyponormal operators and Weyl type theorems for algebraically quasi-M-hyponormal operators, respectively. It is also proved that if T is an algebraically quasi-M -hyponormal operator, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

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7

Mecheri, Salah. "Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators." Georgian Mathematical Journal 29, no. 2 (2021): 233–44. http://dx.doi.org/10.1515/gmj-2021-2124.

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Abstract The question whether every operator on infinite-dimensional Hilbert space 𝐻 has a nontrivial invariant subspace or a nontrivial hyperinvariant subspace is one of the most difficult problems in operator theory. This problem is open for more than half a century. A subnormal operator has a nontrivial invariant subspace, but the existence of nontrivial invariant subspace for a hyponormal operator 𝑇 still open. In this paper we give an affirmative answer of the existence of a nontrivial hyperinvariant subspace for a hyponormal operator. More generally, we show that a large classes of opera

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8

Mecheri, S., and T. Prasad. "Fuglede – Putnam type theorems for extension of -hyponormal operators." Ukrains’kyi Matematychnyi Zhurnal 74, no. 1 (2022): 89–98. http://dx.doi.org/10.37863/umzh.v74i1.2355.

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UDC 517.9 We consider -quasi--hyponormal operator suchthat for some and prove the Fuglede–Putnam type theorem when adjoint of is -quasi--hyponormal or dominant operators.We also show that two quasisimilar -quasi--hyponormal operators have equal essential spectra.

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9

Duggal, B. P. "A remark on the essential spectra of quasi-similar dominant contractions." Glasgow Mathematical Journal 31, no. 2 (1989): 165–68. http://dx.doi.org/10.1017/s0017089500007680.

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We consider operators, i.e. bounded linear transformations, on an infinite dimensional separable complex Hilbert space H into itself. The operator A is said to be dominant if for each complex number λ there exists a number Mλ(≥l) such that ∥(A – λ)*x∥ ≤ Mλ∥A – λ)x∥ for each x∈H. If there exists a number M≥Mλ for all λ, then the dominant operator A is said to be M-hyponormal. The class of dominant (and JW-hyponormal) operators was introduced by J. G. Stampfli during the seventies, and has since been considered in a number of papers, amongst then [7], [11]. It is clear that a 1-hyponormal is hyp

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10

Lauric, Vasile. "Some remarks on the invariant subspace problem for hyponormal operators." International Journal of Mathematics and Mathematical Sciences 28, no. 6 (2001): 359–65. http://dx.doi.org/10.1155/s0161171201011966.

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We make some remarks concerning the invariant subspace problem for hyponormal operators. In particular, we bring together various hypotheses that must hold for a hyponormal operator without nontrivial invariant subspaces, and we discuss the existence of such operators.

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