A new characterization of Anderson’s inequality in C 1-classes

Mecheri, Salah

doi:10.1007/s10587-007-0107-z

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…A similar result for the orthogonality in unitarily invariant norms defined on the norm ideals of K(H) is given in [54, Theorem 1]. For related study on derivations, elementary operators and orthogonality in these normed spaces, see [27,50,56,62,63,64,65,66,92,93,94].…”

Section: Using This One Obtainsmentioning

confidence: 78%

Birkhoff-James orthogonality and applications : A survey

Grover¹,

Sushil²

2020

Preprint

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In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained.

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Section: Using This One Obtainsmentioning

confidence: 78%

Birkhoff-James orthogonality and applications : A survey

Grover¹,

Sushil²

2020

Preprint

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“…e main purpose of this paper is to characterize the elements that are orthogonal to the range of arbitrary elementary operators defined on C 1 (H) in nonsmoothness case and give a counter example to the results of S. Mecheri and M. Bounkhel [10].…”

Section: Definition 2 If Ementioning

confidence: 99%

“…We recall that the characterization of the points in C 1 (H) that are orthogonal to the range of the elementary operators has been carried out by certain authors for smooth case and for certain kind of elementary operators [9,11]. In nonsmoothness case, S. Mecheri and M. Bounkhel [10] have obtained the following result.…”

Section: □ Corollary 2 Let a Be A Normal Operator In B(h) With σ Pr (A) � ∅ And S ∉ Kerδmentioning

confidence: 99%

Range-Kernel Orthogonality and Elementary Operators: The Nonsmoothness Case

2020

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The characterization of the points in C1ℋ, the trace class operators, that are orthogonal to the range of elementary operators has been carried out for certain kinds of elementary operators by many authors in the smooth case. In this note, we study that the characterization is a problem in nonsmoothness case for general elementary operators, and we give a counter example to S. Mecheri and M. Bounkhel results.

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Weyl Type Theorems for Posinormal Operators

Mecheri¹,

Seddik²

2008

Mathematical Proceedings of the Royal Irish Academy

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A new characterization of Anderson’s inequality in C 1-classes

Cited by 3 publications

References 5 publications

Birkhoff-James orthogonality and applications : A survey

Birkhoff-James orthogonality and applications : A survey

Range-Kernel Orthogonality and Elementary Operators: The Nonsmoothness Case

Weyl Type Theorems for Posinormal Operators

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