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- W47340958 abstract "In this chapter, we study completely bounded homomorphisms u: (Arightarrow B(H)) when (A subset B(mathcal{H})) is a subalgebra. We first consider the case when H and (mathcal{H}) are Banach spaces but mostly concentrate on the Hilbert space case. In the latter case, we prove the Jundamental result that a unital homomorphism is completely bounded iff it is similar to a completely contractive one. Let (delta: A rightarrow B(H)) be a derivation on a C*-algebra. We show that (delta) is completely bounded iff it is inner. When A is the disc algebra, we prove that an operator T on H is similar to a contraction iff it is completely polynomially bounded, or in other words iff the associated homomorphism (frightarrow f (T)) is completely bounded. We discuss a variant for operators on a Banach space and give several related facts. Finally, we give examples showing that a bounded (and actually contractive) unital homomorphism on a uniform algebra is not necessarily completely bounded." @default.
- W47340958 created "2016-06-24" @default.
- W47340958 creator A5035197493 @default.
- W47340958 date "1996-01-01" @default.
- W47340958 modified "2023-09-26" @default.
- W47340958 title "Completely bounded homomorphisms and derivations" @default.
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- W47340958 doi "https://doi.org/10.1007/978-3-662-21537-1_5" @default.
- W47340958 hasPublicationYear "1996" @default.
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