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Relations Between Generalized Growth Conditions and Several Classes of Convexoid Operators

Published online by Cambridge University Press:  20 November 2018

Takayuki Furuta
Takayuki Furuta*
Affiliation:
Hirosaki University, Bunkyo-Cho 3, Hirosaki, Aomori-Ken 036, Japan
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In this paper we shall discuss some classes of bounded linear operators on a complex Hilbert space. If T is a bounded linear operator T acting on the complex Hilbert space H, then the following two inequalities always hold:

where σ(T) indicates the spectrum of T, W(T) denotes the numerical range of T defined by W(T) = {(Tx, x) : ||x|| = 1 and x ∊ H} and means the closure of W(T) respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 1010 - 1030
Copyright
Copyright © Canadian Mathematical Society 1977

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