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Completely bounded Banach-Mazur distance†

Published online by Cambridge University Press:  20 January 2009

Chun Zhang
Chun Zhang
Affiliation:
Department of Mathematics, The University of Houston, Houston, TX 77204, U.S.A.
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Abstract

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Analogous to the Banach-Mazur distance between Banach spaces, we study the completely bounded Banach-Mazur distance between operator spaces.

In many cases of Banach spaces and Hilbert spaces we show that the infimum is attained when T is the identity map, and X, Y have the same base space. This provides a machinery to compute and estimate dcb(X, Y). Later, using symmetric norming functions we construct counterexamples to show that distinct infinite dimensional homogeneous operator spaces may have finite cb-distance, and that two homogeneous Hilbertian operator spaces may not coincide even if they coincide over all 2-dimensional subspaces.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 247 - 260
Copyright
Copyright © Edinburgh Mathematical Society 1997

Footnotes

†

This is part of author's Ph.D. thesis directed by Professor Vern Paulsen. The author wants to express his sincerest gratitude.

References

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