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On Banach algebra elements of thin numerical range

Published online by Cambridge University Press:  24 October 2008

R. R. Smith
R. R. Smith
Affiliation:
Texas A & M University, College Station, Texas 77843
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Among the elements of a complex unital Banach algebra the real subspace of hermitian elements deserves special attention. This forms the natural generalization of the set of self-adjoint elements in a C*-algebra and exhibits many of the same properties. Two equivalent definitions may be given: if W(h) ⊂ , where W(h) denotes the numerical range of h (7), or if ║eiλh║ = 1 for all λ ∈ . In this paper some related subsets are introduced and studied. For δ ≥ 0, an element is said to be a member of if the condition

is satisfied. These may be termed the elements of thin numerical range if δ is small.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 71 - 83
Copyright
Copyright © Cambridge Philosophical Society 1979

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