Topological and bornological characterisations of ideals in von Neumann algebras: I |
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Authors: | Graeme West |
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Affiliation: | (1) Dept Math and Computer Science, Kent State University, 44242 Kent, OH, USA |
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Abstract: | ![]() Suppose is a von Neumann algebra on a Hilbert space and is any ideal in . We determine a topology on , for which the members of that are to norm continuous are exactly those in ; and a bornology on such that the elements of which map the unit ball to an element of , equivalently those members of that are norm to bounded, are exactly those in . This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces. |
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Keywords: | primary 46L10 secondary 46A17 47D50 |
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