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Orthogonality preserving linear maps on group algebras

Published online by Cambridge University Press:  05 March 2015

J. ALAMINOS ,
J. EXTREMERA  and
A. R. VILLENA
J. ALAMINOS
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. e-mail: avillena@ugr.es
J. EXTREMERA
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. e-mail: avillena@ugr.es
A. R. VILLENA
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. e-mail: avillena@ugr.es
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Abstract

We consider several types of orthogonality conditions on the group algebra L1(G) of a locally compact group G such as f$\ast $g = 0, f$\ast $g☆ = 0, f☆$\ast $g = 0, f$\ast $g = g$\ast $f = 0 and f$\ast $g☆ = g☆$\ast $f = 0, and we describe the linear maps Φ: L1(G) → L1(H) between the group algebras of locally compact groups G and H that take orthogonal functions of L1(G) into orthogonal functions of L1(H). Roughly speaking, they are weighted homomorphisms in the case where we are concerned with the one-sided orthogonality conditions and weighted Jordan homomorphisms in the case where we treat the two-sided orthogonality conditions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 3 , May 2015 , pp. 493 - 504
Copyright
Copyright © Cambridge Philosophical Society 2015 

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