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Paranormal operators on Banach spaces

Published online by Cambridge University Press:  17 April 2009

N.N. Chourasia  and
P.B. Ramanujan
N.N. Chourasia
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388120, Gujarat, India.
P.B. Ramanujan
Affiliation:
Department of Mathematics, Saurashtra University, Rajkot - 360005, Gujarat, India.
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Abstract

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In this note we show that a paranormal operator T on a Banach space satisfies Weyl's theorem. This is accomplished by showing that

(i) every isolated point of its spectrum is an eigenvalue and the corresponding eigenspace has invariant complement,

(ii) for α ≠ 0, Ker(T-α) ⊥ Ker (T-β) (in the sense of Birkhoff) whenever β ≠ α.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 2 , May 1980 , pp. 161 - 168
Copyright
Copyright © Australian Mathematical Society 1980

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