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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Operator ideals and operator spaces


Authors: D. Benjamin Mathes and Vern I. Paulsen
Journal: Proc. Amer. Math. Soc. 123 (1995), 1763-1772
MSC: Primary 47D50; Secondary 46B28, 46L05, 47B10
MathSciNet review: 1242095
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Abstract: We prove that every full symmetrically normed ideal of operators on a Hilbert space is realizable as the set of completely bounded maps between two homogeneous operator Hilbert spaces, with the c.b. norm equivalent to (but in general not equal to) the symmetric norm. We show that one can have equality of the c.b. norm and the symmetric norm if one leaves the category of operator spaces and passes to a slightly larger category.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1242095-X
Article copyright: © Copyright 1995 American Mathematical Society