Distortions on Schatten Classes Cp
Schatten classes Cp of operators on a Hilbert space are classical non-commutative Banach space analogues of spaces lp. The result by Odell and Schlumprecht [OS] that spaces lp are arbitrarily distortable for 1 <p< ∞, suggests that a similar situation might be true for Schatten classes as well. In this note we prove that it is indeed so: for 1 <p< ∞, spaces Cp are arbitrarily distortable.
KeywordsOrthogonal Projection Successive Operator Partial Isometry Distorted Norm General Banach Space
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