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Some inequalities for norm unitaries in Banach algebras

Published online by Cambridge University Press:  20 January 2009

M. J. Crabb  and
J. Duncan
M. J. Crabb
Affiliation:
University of Glasgow
J. Duncan
Affiliation:
University of Stirling
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Let A be a complex unital Banach algebra. An element u∈A is a norm unitary if

(For the algebra of all bounded operators on a Banach space, the norm unitaries arethe invertible isometries.) Given a norm unitary u∈A, we have Sp(u)⊃Γ, where Sp(u) denotes the spectrum of u and Γ denotes the unit circle in C. If Sp(u)≠Γ we may suppose, by replacing eiθu, that . Then there exists h ∈ A such that

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 1 , March 1978 , pp. 17 - 23
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

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