Birkhoff–James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs

Ljiljana Arambašić; Alexander Guterman; Bojan Kuzma; Svetlana Zhilina

doi:10.1007/978-3-031-02104-6_8

Birkhoff–James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs

Ljiljana Arambašić, Alexander Guterman, Bojan Kuzma, Svetlana Zhilina

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

We present Birkhoff–James orthogonality from historical perspectives to the current development. We compare it with some other orthogonalities, present its properties and its applications, and review the characterizations of Birkhoff–James orthogonality in classical Banach spaces like (ℋ), C^∗-algebras, Hilbert C^∗-modules, or the space of rectangular matrices normed with Schatten norms. We also present the results on characterizations of preservers of Birkhoff–James orthogonality and, by devising a directed graph of the relation, show that in smooth spaces it can completely determine the norm up to (conjugate) linear isometry. Most, though not all, of the results that we state are supplied with (sketches of) the proof.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	255-302
Number of pages	48
DOIs	https://doi.org/10.1007/978-3-031-02104-6_8
State	Published - 2022
Externally published	Yes

Publication series

Name	Trends in Mathematics
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Birkhoff–James orthogonality
C-algebra
Clique
Graph
Hilbert C-module
Normed vector space
Preservers

Access to Document

10.1007/978-3-031-02104-6_8

Cite this

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Birkhoff–James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs

Abstract

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Keywords

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