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Extreme Points of Positive Functionals and Spectral States on Real Banach Algebras

Published online by Cambridge University Press:  20 November 2018

Anand Srivastav
Anand Srivastav*
Affiliation:
Research Institute of Discrete Mathematics, University of Bonn, Nassestr. 2, W-5 300 Bonn 1, Germany
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Abstract

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Extreme points of positive functionals and spectral states on real commutative Banach algebras are investigated and characterized as multiplicative functionals extending the well-known results from complex to real Banach algebras. As an application a new and short proof of the existence of the Shilov boundary of a real commutative Banach algebra with nonempty maximal ideal space is given.

Keywords

Primary: 46J0546J20Real Banach algebrapositive functionalsmaximal idealsShilov boundary
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 856 - 866
Copyright
Copyright © Canadian Mathematical Society 1992

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