Orthograph related to mutual strong Birkhoff–James orthogonality in C∗ -algebras

Ljiljana Arambašić; Alexander Guterman; Bojan Kuzma; Rajna Rajić; Svetlana Zhilina

doi:10.1007/s43037-020-00074-x

Orthograph related to mutual strong Birkhoff–James orthogonality in C^∗ -algebras

Ljiljana Arambašić, Alexander Guterman, Bojan Kuzma, Rajna Rajić, Svetlana Zhilina

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

Abstract

We study the relation of mutual strong Birkhoff–James orthogonality in two classical C^∗-algebras: the C^∗-algebra B(H) of all bounded linear operators on a complex Hilbert space H and the commutative, possibly nonunital, C^∗-algebra. With the help of the induced graph it is shown that this relation alone can characterize right invertible elements. Moreover, in the case of commutative unital C^∗-algebras, it can detect the existence of a point with a countable local basis in the corresponding compact Hausdorff space.

Original language	English
Pages (from-to)	1751-1772
Number of pages	22
Journal	Banach Journal of Mathematical Analysis
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/s43037-020-00074-x
State	Published - 1 Sep 2020
Externally published	Yes

Keywords

(strong) Birkhoff–James orthogonality
C-algebra
Diameter
Graph
Right invertible element

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory

Access to Document

10.1007/s43037-020-00074-x

Cite this

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title = "Orthograph related to mutual strong Birkhoff–James orthogonality in C∗ -algebras",

abstract = "We study the relation of mutual strong Birkhoff–James orthogonality in two classical C∗-algebras: the C∗-algebra B(H) of all bounded linear operators on a complex Hilbert space H and the commutative, possibly nonunital, C∗-algebra. With the help of the induced graph it is shown that this relation alone can characterize right invertible elements. Moreover, in the case of commutative unital C∗-algebras, it can detect the existence of a point with a countable local basis in the corresponding compact Hausdorff space.",

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AU - Arambašić, Ljiljana

AU - Guterman, Alexander

AU - Kuzma, Bojan

AU - Rajić, Rajna

AU - Zhilina, Svetlana

PY - 2020/9/1

Y1 - 2020/9/1

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AB - We study the relation of mutual strong Birkhoff–James orthogonality in two classical C∗-algebras: the C∗-algebra B(H) of all bounded linear operators on a complex Hilbert space H and the commutative, possibly nonunital, C∗-algebra. With the help of the induced graph it is shown that this relation alone can characterize right invertible elements. Moreover, in the case of commutative unital C∗-algebras, it can detect the existence of a point with a countable local basis in the corresponding compact Hausdorff space.

KW - (strong) Birkhoff–James orthogonality

KW - C-algebra

KW - Diameter

KW - Graph

KW - Right invertible element

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EP - 1772

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

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