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Some special bounded homomorphisms of a uniform algebra
Title:  Some special bounded homomorphisms of a uniform algebra 
Authors:  Nakazi, T. Browse this author 
Issue Date:  1Feb1999 
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 11I>II of q, equal to the completely bounded norm 11I>llcb ? In some special cases we answer this question. Suppose q, is pcontractive (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 pdilation. If q, is a pcontractive homomorphism then 1\I>\\ == max(l, p) and if it has a pdilation then 11I>llcb == max(l, p). Moreover we give a new example of a hypoDirichlet 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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