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Commuting Dilations and Uniform Algebras

Published online by Cambridge University Press:  20 November 2018

Takahiko Nakazi
Takahiko Nakazi*
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan
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Let X be a compact Hausdorff space, let C(X) be the algebra of complex-valued continuous functions on X, and let A be a uniform algebra on X. Fix a nonzero complex homomorphism τ on A and a representing measure m for τ on X. The abstract Hardy space Hp = Hp(m), 1 ≤ p ≤ ∞, determined by A is defined to the closure of Lp = Lp(m) when p is finite and to be the weak*-closure of A in L∞ = L∞(m) p = ∞.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 776 - 789
Copyright
Copyright © Canadian Mathematical Society 1990

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