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

University of Zagreb
Lomonosov Moscow State University
Moscow Center for Fundamental and Applied Mathematics
Moscow Institute of Physics and Technology
University of Primorska
Institute of Mathematics, Physics, and Mechanics

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

12 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2020, Tusi Mathematical Research Group (TMRG).

Funding

The authors thank the anonymous referees for useful comments and suggestions that helped improve the presentation from the original manuscript. Ljiljana Arambašić and Rajna Rajić were fully supported by the Croatian Science Foundation under the project IP-2016-06-1046. Alexander Guterman and Svetlana Zhilina were fully supported by RSF grant 17-11-01124. Bojan Kuzma acknowledges the financial support from the Slovenian Research Agency, ARRS (research core funding No. P1-0222 and No. P1-0285).

Funders	Funder number
Javna Agencija za Raziskovalno Dejavnost RS	P1-0285, P1-0222
Hrvatska Zaklada za Znanost	IP-2016-06-1046
Russian Science Foundation	17-11-01124

Keywords

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

Access to Document

10.1007/s43037-020-00074-x

Cite this

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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 - Zhilina, Svetlana

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