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On totally paranormal operators

Published online by Cambridge University Press:  17 April 2009

Christoph Schmoeger
Christoph Schmoeger
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany e-mail: christoph.schmoeger@math.uni-karlsruhe.de
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A continuous linear operator on a complex Banach space is said to be paranormal if ‖Tx‖2 ≤ ‖T2x‖ ‖x‖ for all x ∈ X. T is called totally paranormal if T–λ is paranormal for every λ ∈ C. In this paper we investigate the class of totally paranormal operators. We shall see that Weyl's theorem holds for operators in this class. We also show that for totally paranormal operators the Weyl spectrum satisfies the spectral mapping theorem. In Section 5 of this paper we investigate the operator equations eT = eS and eTeS = eSeT for totally paranormal operators T and S.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 425 - 441
Copyright
Copyright © Australian Mathematical Society 2002

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