The Birkhoff-James orthogonality of operators on infinite dimensional Banach spaces

Sun Kwang Kim; Han Ju Lee

doi:10.1016/j.laa.2019.08.012

The Birkhoff-James orthogonality of operators on infinite dimensional Banach spaces

Sun Kwang Kim, Han Ju Lee

Department of Mathematics Education

Chungbuk National University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-Šemrl property. We first prove that every functional on a Banach space X has the Bhatia-Šemrl property if and only if X is reflexive. We also find some geometric conditions of Banach space which ensure the denseness of operators with Bhatia-Šemrl property. Finally, we investigate operators with the Bhatia-Šemrl property when a domain space is L₁[0,1] or C[0,1].

Original language	English
Pages (from-to)	440-451
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	582
DOIs	https://doi.org/10.1016/j.laa.2019.08.012
State	Published - 1 Dec 2019

Keywords

Banach space
Birkhoff-James orthogonality
The Bhatia-Šemrl property

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10.1016/j.laa.2019.08.012

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title = "The Birkhoff-James orthogonality of operators on infinite dimensional Banach spaces",

abstract = "We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-{\v S}emrl property. We first prove that every functional on a Banach space X has the Bhatia-{\v S}emrl property if and only if X is reflexive. We also find some geometric conditions of Banach space which ensure the denseness of operators with Bhatia-{\v S}emrl property. Finally, we investigate operators with the Bhatia-{\v S}emrl property when a domain space is L1[0,1] or C[0,1].",

keywords = "Banach space, Birkhoff-James orthogonality, The Bhatia-{\v S}emrl property",

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AU - Lee, Han Ju

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N2 - We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-Šemrl property. We first prove that every functional on a Banach space X has the Bhatia-Šemrl property if and only if X is reflexive. We also find some geometric conditions of Banach space which ensure the denseness of operators with Bhatia-Šemrl property. Finally, we investigate operators with the Bhatia-Šemrl property when a domain space is L1[0,1] or C[0,1].

AB - We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-Šemrl property. We first prove that every functional on a Banach space X has the Bhatia-Šemrl property if and only if X is reflexive. We also find some geometric conditions of Banach space which ensure the denseness of operators with Bhatia-Šemrl property. Finally, we investigate operators with the Bhatia-Šemrl property when a domain space is L1[0,1] or C[0,1].

KW - Banach space

KW - Birkhoff-James orthogonality

KW - The Bhatia-Šemrl property

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M3 - Article

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SN - 0024-3795

VL - 582

SP - 440

EP - 451

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The Birkhoff-James orthogonality of operators on infinite dimensional Banach spaces

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Keywords

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