Extension of Finite Rank Operators and Local Structures in Operator Ideals

1999/02/23 by F. Oertel, Oertel, F.
Mathematics · #46M05 #47D50 (Primary) 47A80 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46M05 #msc:47A80 #msc:47D50

paper · pdf · doi:10.48550/arxiv.math/9902135

LaTeX 2e, 26 pages

arxiv created 1999/02/23 · arxiv updated 2009/11/30

Abstract

We develop general techniques and present an approach to solve the problem of constructing a maximal Banach ideal (\frak A,\bf A) which does not satisfy a transfer of the norm estimation in the principle of local reflexivity to its norm \bf A. This approach leads us to the investigation of product operator ideals containing \frak L₂ (the collection of all Hilbertian operators) as a factor. Using the local properties of such operator ideals -- which are typical examples of ideals with property (I) and property (S) --, trace duality and an extension of suitable finite rank operators even enable us to show that \frak L_∞ cannot be totally accessible -- answering an open question of Defant and Floret.

Related

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• A Short Note on some open problems in the geometry of operator ideals
• Local properties of accessible injective operator ideals
• Operators with extension property and the principle of local reflexivity
• On normed products of operator ideals which contain \frakL₂ as a factor