p ‐nuclear operators in the sense of Grothendieck

2010/01/29 by Aicke Hinrichs, Albrecht Pietsch · 2 citations
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paper · doi:10.1002/mana.200910128

openalex publication_date 2010/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

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)

Citations

• Approximation spaces
• Cp
• The approximation property does not imply the bounded approximation property

Cited by

• Lp-nuclearity, traces, and Grothendieck–Lidskii formula on compact Lie groups
• Nuclear operators between Banach spaces [wikipedia]

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