Direct Sums of Operator Spaces |
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Authors: | Oikhberg Timur |
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Institution: | Department of Mathematics, University of Texas Austin, TX 78712, USA, timur{at}math.utexas.edu |
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Abstract: | It is proved that if X and Y are operator spaces such that everycompletely bounded operator from X into Y is completely compactand Z is a completely complemented subspace of X Y, then thereexists a completely bounded automorphism : X Y X Y with completelybounded inverse such that Z = X0 Y0, where X0 and Y0 are completelycomplemented subspaces of X and Y, respectively. If X and Yare homogeneous, the existence is proved of such a under aweaker assumption that any operator from X to Y is strictlysingular. An upper estimate is obtained for || ||cb|| 1||cbif X and Y are separable homogeneous Hilbertian operator spaces.Also proved is the uniqueness of a completely unconditionalbasis in X Y if X and Y satisfy certain conditions. |
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