On Homomorphisms of Douglas Algebras
Alexander Brudnyi

TL;DR
This paper investigates homomorphisms between Douglas algebras and semisimple Banach algebras, utilizing the structure of continuous mappings into maximal ideal spaces, revealing density and trivial homotopy groups.
Contribution
It provides new insights into the structure of homomorphisms between Douglas algebras and semisimple Banach algebras, especially regarding the topology of continuous mappings and homotopy groups.
Findings
Density of continuous mappings from Z to D in pointwise topology
Trivial homotopy groups of the maximal ideal space
Structural results on homomorphisms between Douglas algebras
Abstract
The paper describes homomorphisms between Douglas algebras and some semisimple Banach algebras. The main tool is a result on the structure of the space of continuous mappings from a connected first-countable space to the maximal ideal space of the algebra of bounded holomorphic functions on the unit disk . In particular, it is shown that the space of continuous mappings from to is dense in the topology of pointwise convergence in and the homotopy groups of are trivial.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
