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Norm Convergence of Tn

Published online by Cambridge University Press:  20 November 2018

Glenn R. Luecke
Glenn R. Luecke*
Affiliation:
Iowa State University, Ames, Iowa 50011
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Throughout this paper X will denote a complex Banach space and all operators T will be assumed to be continuous linear transformations from X into X. If T is an operator then ┘(T), γ(T), and R(T) will denote the spectrum of T, the spectral radius of T, and range of T, respectively. This paper contains necessary and sufficient conditions for the (norm) convergence of {Tn} when T is an operator on X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1340 - 1344
Copyright
Copyright © Canadian Mathematical Society 1977

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