We study analogues, in the Lipschitz and Operator Spaces categories, of several classical ideals of operators between Banach spaces. We introduce the concept of a Banach-space-valued molecule, which is used to develop a duality theory for several nonlinear ideals of operators including the ideal of Lipschitz p-summing operators and the ideal of factorization through a subset of a Hilbert space. We prove metric characterizations of p-convex operators, and also of those with Rademacher type and cotype. Lipschitz versions of p-convex and p-concave operators are also considered. We introduce the ideal of Lipschitz (q,p)-mixing operators, of which we prove several characterizations and give applications. Finally the ideal of completely (q,p)-mixing maps between operator spaces is studied, and several characterizations are given. They are used to prove an operator space version of Pietsch's composition theorem for p-summing operators.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2012-08-11642 |
| Date | 2012 August 1900 |
| Creators | Chavez Dominguez, Javier |
| Contributors | Johnson, William B. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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