Linear disjointness preservers of operator algebras and related structures

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

doi:10.14232/actasm-018-267-7

Linear disjointness preservers of operator algebras and related structures

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

Department of Mathematics

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

19 Citations (Scopus)

Abstract

We survey some recent studies of linear zero product or orthogonality preservers between C^∗/W^∗-algebras, their dual or predual spaces, and holomorphic disjointness preservers of C^∗-algebras. Such maps are expected to provide algebra or linear Jordan (∗-) homomorphisms between the underlying operator algebras. We also study orthogonality preservers between Hilbert C^∗-modules and Fourier algebras. A few open problems are stated.

Original language	English
Pages (from-to)	277-307
Number of pages	31
Journal	Acta Scientiarum Mathematicarum
Volume	84
Issue number	1-2
DOIs	https://doi.org/10.14232/actasm-018-267-7
Publication status	Published - 2018

User-Defined Keywords

Fourier algebras
Hilbert C∗-modules
Holomorphic maps of C∗-algebras
Jordan homomorphisms
Orthogonality preservers
Zero product preservers

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10.14232/actasm-018-267-7

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title = "Linear disjointness preservers of operator algebras and related structures",

abstract = "We survey some recent studies of linear zero product or orthogonality preservers between C∗/W∗-algebras, their dual or predual spaces, and holomorphic disjointness preservers of C∗-algebras. Such maps are expected to provide algebra or linear Jordan (∗-) homomorphisms between the underlying operator algebras. We also study orthogonality preservers between Hilbert C∗-modules and Fourier algebras. A few open problems are stated.",

keywords = "Fourier algebras, Hilbert C∗-modules, Holomorphic maps of C∗-algebras, Jordan homomorphisms, Orthogonality preservers, 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",

doi = "10.14232/actasm-018-267-7",

language = "English",

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pages = "277--307",

journal = "Acta Scientiarum Mathematicarum",

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TY - JOUR

T1 - Linear disjointness preservers of operator algebras and related structures

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

Y1 - 2018

N2 - We survey some recent studies of linear zero product or orthogonality preservers between C∗/W∗-algebras, their dual or predual spaces, and holomorphic disjointness preservers of C∗-algebras. Such maps are expected to provide algebra or linear Jordan (∗-) homomorphisms between the underlying operator algebras. We also study orthogonality preservers between Hilbert C∗-modules and Fourier algebras. A few open problems are stated.

AB - We survey some recent studies of linear zero product or orthogonality preservers between C∗/W∗-algebras, their dual or predual spaces, and holomorphic disjointness preservers of C∗-algebras. Such maps are expected to provide algebra or linear Jordan (∗-) homomorphisms between the underlying operator algebras. We also study orthogonality preservers between Hilbert C∗-modules and Fourier algebras. A few open problems are stated.

KW - Fourier algebras

KW - Hilbert C∗-modules

KW - Holomorphic maps of C∗-algebras

KW - Jordan homomorphisms

KW - Orthogonality preservers

KW - Zero product preservers

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U2 - 10.14232/actasm-018-267-7

DO - 10.14232/actasm-018-267-7

M3 - Journal article

AN - SCOPUS:85045732676

SN - 0001-6969

VL - 84

SP - 277

EP - 307

JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

IS - 1-2

ER -

Linear disjointness preservers of operator algebras and related structures

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