2019-10-18T01:53:34Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/691932018-04-25T23:44:07Zhdl_2115_45007hdl_2115_116Some special bounded homomorphisms of a uniform algebraNakazi, T.open access410Let 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.1999-02-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83589http://hdl.handle.net/2115/6919310.14943/83589Hokkaido University Preprint Series in Mathematics443110https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69193/1/pre443.pdfapplication/pdf556.06 KB1999-02-01