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K -- Convex Operators and Walsh Type Norms

✍ Scribed by Aicke Hinrichs

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
647 KB
Volume
208
Category
Article
ISSN
0025-584X

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✦ Synopsis

A celebrated result of G. PISIER states that the notions of B-convexity and Kconvexity coincide for Banach spaces. We complement this in the setting of linear and bounded operators between Banach spaces. Our approach is local and even yields inequalities between gradations of K-convexity norms and Walsh type norms of operators. Our method combines G. PISIER'S original ideas and the main steps in the proof of the Beurling-Kato theorem on extensions of COsemigroups of operators to holomorphic semigroups with the technique of ideal norms.

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Primary: 47D50, 46B07. Keywords and phrases. K -convexity, Bconvexity, Walsh functions.

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