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A Filter Description of the Homomorphisms of H∞

Published online by Cambridge University Press:  20 November 2018

A. Kerr-Lawson
A. Kerr-Lawson*
Affiliation:
University of Waterloo, Waterloo, Ontario
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The algebra of bounded analytic functions on the open unit disk D, usually written H∞ i is a commutative Banach algebra under the supremum norm. Since its compact maximal ideal space M (space of complex homomorphisms) is an extension space of the unit disk, there must be a continuous mapping form βD, the Stone-Čech compactification of D, onto M. R. C. Buck has remarked (4), that this mapping fails to be one-one, in the light of a classical theorem of Pick. If the points of βD are represented by filters of subsets of D, we can identify those filters which are sufficiently close in terms of the hyperbolic metric on D in an attempt to get a one-one correspondence between filters and points of M.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 734 - 757
Copyright
Copyright © Canadian Mathematical Society 1965

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