On Some Classical Banach Space Concepts in Operator Space Theory

126 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005.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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD