Every completely polynomially bounded operator is similar to a contraction |
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Authors: | Vern I Paulsen |
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Affiliation: | Department of Mathematics, University of Houston, Houston, Texas 77004 USA |
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Abstract: | It is proved that a bounded operator on a Hilbert space is similar to a contraction if and only if it is completely polynomially bounded. This gives a partial answer to Problem 6 of Halmos (Bull. Amer. Math. Soc.76 (1970). 877–933). The set of completely bounded maps between C1-algebras is studied to obtain some structure, representation, and extension theorems for this class of maps. These allow a characterization of the completely bounded representations, on a Hilbert space, of any subalgebra of a C1-algebra to be obtained. The result in the title follows by applying this characterization to the disk algebra. |
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