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p -nuclear operators in the sense of Grothendieck

✍ Scribed by Aicke Hinrichs; Albrecht Pietsch

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
309 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The by now classical theory of p ‐nuclear operators with 0 < p ≤ 1 was founded in Grothendieck's thesis (1953). Since that time only little progress has been achieved. This article describes the present state of the art. We improve Grothendieck's multiplication theorem, characterize the p ‐integral operators, and give a long list of challenging open problems. The abstract theory is illustrated by considering the identity map and the discrete Fourier transform from l~a~^n^ onto l~b~^n^ with 1 ≤ a, b ≤ ∞ (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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