Twisting operator spaces
Copyright policy )Twisting operator spaces
In this work we study the following three space problem for operator spaces: if X is an operator space with base space isomorphic to a Hilbert space and X contains a completely isomorphic copy of the operator Hilbert space OH with respective quotient also completely isomorphic to OH, must X be completely isomorphic to OH? This problem leads us to the study of short exact sequences of operator spaces, more specifically those induced by complex interpolation, and their splitting. We show that the answer to the three space problem is negative, giving two different solutions.
37 pages
- UNIVERSIDADE DE SAO PAULO Brazil
Mathematics - Functional Analysis, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), Abstract operator algebras on Hilbert spaces, three-space problem, operator spaces, Operator spaces (= matricially normed spaces), Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), 47L25, 46M18, Functional Analysis (math.FA)
Mathematics - Functional Analysis, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), Abstract operator algebras on Hilbert spaces, three-space problem, operator spaces, Operator spaces (= matricially normed spaces), Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), 47L25, 46M18, Functional Analysis (math.FA)
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