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Some special bounded homomorphisms of a uniform algebra

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83589

Title: Some special bounded homomorphisms of a uniform algebra
Authors: Nakazi, T. Browse this author
Issue Date: 1-Feb-1999
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 443
Start Page: 1
End Page: 10
Abstract: Let L(H) be the algebra of all bounded linear operators on a Hilbert space H and let A be a uniform algebra. In this paper we study the following questions. When is a unital bounded homomorphism q, of A in L(H) completely bounded ? When is the norm 11-I>II of q, equal to the completely bounded norm 11-I>llcb ? In some special cases we answer this question. Suppose q, is p-contractive (0 < p < oo) where 4> is contractive if p == 1. We show that if A is a Dirichlet algebra or dim A/ ker q, == 2 then q, has a p-dilation. If q, is a p-contractive homomorphism then 1\-I>\\ == max(l, p) and if it has a p-dilation then 11-I>llcb == max(l, p). Moreover we give a new example of a hypo-Dirichlet algebra in which a unital contractive homomorphism has a contractive dilation.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69193
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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