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Diameter-preserving linear bijections of function spaces

Part of: Special classes of linear operators Linear function spaces and their duals Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  09 April 2009

T. S. S. R. K. Rao  and
A. K. Roy
T. S. S. R. K. Rao
Affiliation:
Statistics and Mathematics Unit Indian Statistical Institute R. V. College PostBangalore 560 059India e-mail: tss@isibang.ac.in
A. K. Roy
Affiliation:
Statistics and Mathematics Unit Indian Statistical Institute203 B. T. Road Calcutta 700 035India e-mail: ashoke@isical.ac.in
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Abstract

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In this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

MSC classification

Secondary: 46J10: Banach algebras of continuous functions, function algebras 46E40: Spaces of vector- and operator-valued functions 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 3 , June 2001 , pp. 323 - 336
Copyright
Copyright © Australian Mathematical Society 2001

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