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p ‐nuclear operators in the sense of Grothendieck
Author(s) -
Hinrichs Aicke,
Pietsch Albrecht
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910128
Subject(s) - mathematics , multiplication (music) , identity (music) , pure mathematics , state (computer science) , fourier transform , algebra over a field , mathematical analysis , combinatorics , algorithm , aesthetics , philosophy
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)