On Some Classical Banach Space Concepts in Operator Space Theory
For the second project, Junge and Xu independently demonstrated recently that the nth-dimensional operator Hilbert space OHn is a subspace of an operator space which is completely isomorphic to a completely complemented subspace of a non-commutative Lp space over a QWEP separable type III factor. Using this, we proved that the completely p-summing norm of the identity map on OHn is bounded by n1+2p -1lnn up to constants independent of 1 < p < 2. An application to the completely (2, p)-mixing constant of OHn is given.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign