Subspace structure of some operator and Banach spaces

2010/09/18 by Timur Oikhberg, Oikhberg, Timur, Christian Rosendal +1
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1009.3591

openalex publication_date 2010/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete \ks. We also investigate some interesting properties of completely unconditional bases of the spaces from this family. In the Banach space setting, we construct a space for which the relation of isometry of subspaces is equivalent to equality of real numbers.

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