Disjointness preservers of AW⁎-algebras

Jung Hui Liu; Chun Yen Chou; Ching Jou Liao; Ngai Ching Wong

doi:10.1016/j.laa.2018.04.012

Disjointness preservers of AW^⁎-algebras

Jung Hui Liu, Chun Yen Chou^*, Ching Jou Liao, Ngai Ching Wong

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

Abstract

In this paper, we study bijective linear maps θ:A→B between AW^⁎-algebras preserving either zero products or range orthogonality. Such a map is automatically continuous, and provides an algebra or a ⁎-algebra isomorphism π(⋅)=θ(⋅)θ^⁎⁎(1)⁻¹ from A onto B. Our results extend previous works for the case of W^⁎-algebras, and also cover such maps between C^⁎-algebras satisfying an extra assumption on preserving abelian C^⁎-subalgebras.

Original language	English
Pages (from-to)	71-84
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	552
DOIs	https://doi.org/10.1016/j.laa.2018.04.012
Publication status	Published - 1 Sept 2018

Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

User-Defined Keywords

Automatic continuity
AW-algebras
C-algebras
Orthogonality preservers
Ring isomorphisms
Zero product preservers

Access to Document

10.1016/j.laa.2018.04.012

Cite this

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title = "Disjointness preservers of AW⁎-algebras",

abstract = "In this paper, we study bijective linear maps θ:A→B between AW⁎-algebras preserving either zero products or range orthogonality. Such a map is automatically continuous, and provides an algebra or a ⁎-algebra isomorphism π(⋅)=θ(⋅)θ⁎⁎(1)−1 from A onto B. Our results extend previous works for the case of W⁎-algebras, and also cover such maps between C⁎-algebras satisfying an extra assumption on preserving abelian C⁎-subalgebras.",

keywords = "Automatic continuity, AW-algebras, C-algebras, Orthogonality preservers, Ring isomorphisms, Zero product preservers",

author = "Liu, {Jung Hui} and Chou, {Chun Yen} and Liao, {Ching Jou} and Wong, {Ngai Ching}",

note = "Funding Information: The first author is supported by Sanming University through Digital Fujian Research Institute for Industrial Energy Big Data, Fujian Province University Key Laboratory for the Analysis and Application of Industry Big Data , Fujian Key Lab of Agriculture IOT Application , and IOT Application Engineering Research Center of Fujian Province Colleges and Universities .",

year = "2018",

month = sep,

day = "1",

doi = "10.1016/j.laa.2018.04.012",

language = "English",

volume = "552",

pages = "71--84",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

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TY - JOUR

T1 - Disjointness preservers of AW⁎-algebras

AU - Liu, Jung Hui

AU - Chou, Chun Yen

AU - Liao, Ching Jou

AU - Wong, Ngai Ching

N1 - Funding Information: The first author is supported by Sanming University through Digital Fujian Research Institute for Industrial Energy Big Data, Fujian Province University Key Laboratory for the Analysis and Application of Industry Big Data , Fujian Key Lab of Agriculture IOT Application , and IOT Application Engineering Research Center of Fujian Province Colleges and Universities .

PY - 2018/9/1

Y1 - 2018/9/1

N2 - In this paper, we study bijective linear maps θ:A→B between AW⁎-algebras preserving either zero products or range orthogonality. Such a map is automatically continuous, and provides an algebra or a ⁎-algebra isomorphism π(⋅)=θ(⋅)θ⁎⁎(1)−1 from A onto B. Our results extend previous works for the case of W⁎-algebras, and also cover such maps between C⁎-algebras satisfying an extra assumption on preserving abelian C⁎-subalgebras.

AB - In this paper, we study bijective linear maps θ:A→B between AW⁎-algebras preserving either zero products or range orthogonality. Such a map is automatically continuous, and provides an algebra or a ⁎-algebra isomorphism π(⋅)=θ(⋅)θ⁎⁎(1)−1 from A onto B. Our results extend previous works for the case of W⁎-algebras, and also cover such maps between C⁎-algebras satisfying an extra assumption on preserving abelian C⁎-subalgebras.

KW - Automatic continuity

KW - AW-algebras

KW - C-algebras

KW - Orthogonality preservers

KW - Ring isomorphisms

KW - Zero product preservers

UR - http://www.scopus.com/inward/record.url?scp=85045741224&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.04.012

DO - 10.1016/j.laa.2018.04.012

M3 - Journal article

AN - SCOPUS:85045741224

SN - 0024-3795

VL - 552

SP - 71

EP - 84

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -