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Numerical radii of simple powers

โœ Scribed by Vitali Chkliar


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
112 KB
Volume
265
Category
Article
ISSN
0024-3795

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โœฆ Synopsis


A counterexample is given for the conjecture that the numerical radius of the n + lth power of an operator is less than or equal to the numerical radius of the nth power of the same operator if the operator is a contraction.


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In this note, we formulate a theorem giving bounds on the powers of linear operators, in a general Banach space setting. The relevance of the theorem is illustrated by applying it to the Crank-Nicholson method for the numerical solution of the heat equation. This application yields a stability estim