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Normal operators on Banach spaces

Published online by Cambridge University Press:  18 May 2009

Che-Kao Fong
Che-Kao Fong
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S-IAI
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A (bounded, linear) operator H on a Banach space is said to be hermitian if ∥exp(itH)∥ = 1 for all real t. An operator N on is said to be normal if N = H + iK, where H and K are commuting hermitian operators. These definitions generalize those familiar concepts of operators on Hilbert spaces. Also, the normal derivations defined in [1] are normal operators. For more details about hermitian operators and normal operators on general Banach spaces, see [4]. The main result concerning normal operators in the present paper is the following theorem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 2 , July 1979 , pp. 163 - 168
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

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