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Some extremal algebras for hermitians

Published online by Cambridge University Press:  04 June 2001

M. J. Crabb ,
J. Duncan  and
C. M. McGregor
M. J. Crabb
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, Scotland e-mail:m.crabb@maths.gla.ac.uk
J. Duncan
Affiliation:
Department of Mathematical Sciences, SCEN301, University of Arkansas, Fayetteville, AR 72701-1201, USA e-mail:jduncan@comp.uark.edu
C. M. McGregor
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, Scotland e-mail:c.mcgregor@maths.gla.ac.uk
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We study three extremal Banach algebras: (a) generated by two hermitian unitaries; (b) generated by an element of norm 1 all of whose odd positive powers are hermitian; (c) generated by an element of norm 1 all of whose even positive powers are hermitian. In all three cases the numerical range is found for various elements. The second algebra is shown to be isometrically isomorphic to a subalgebra of the first. The third algebra is identified with a space of functions.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 29 - 38
Copyright
2001 Glasgow Mathematical Journal Trust