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Extension of finite rank operators and local structures.
| Content Provider | CiteSeerX |
|---|---|
| Author | Oertel, Frank |
| Abstract | We develop general techniques and present an approach to solve the problem of constructing a maximal Banach ideal (A,A) which does not satisfy a transfer of the norm estimation in the principle of local reflexivity to its norm A. This approach leads us to the investigation of product operator ideals containing 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 L ∞ cannot be totally accessible – answering an open question of Defant and Floret. Key words and phrases: Accessibility, Banach spaces, cotype 2, finite rank operators, Hilbert space factorization, Grothendieck’s Theorem, operator ideals, principle of local |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Finite Rank Operator Local Structure Operator Ideal Hilbert Space Factorization Maximal Banach Ideal Product Operator Ideal Suitable Finite Rank Operator Local Property General Technique Typical Example Banach Space Open Question Trace Duality Local Reflexivity Norm Estimation Hilbertian Operator |
| Content Type | Text |
