Extension of Finite Rank Operators and Local Structures in Operator Ideals

Details Extension of Finite Rank Operators and Local Structures in Operator Ideals Extension of Finite Rank Operators and Local Structures in Operator Ideals

1999-02-23

arxiv.org/abs/math/9902135v1

Mathematics

Functional Analysis

LaTeX 2e, 26 pages

Scientific paper

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 ${\frak L}_2$ (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}_\infty $ cannot be totally accessible -- answering an open question of Defant and Floret.

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