A holomorphic characterization of operator algebras
Matthew Neal, Bernard Russo
TL;DR
This paper provides a holomorphic criterion that characterizes when an operator space can be endowed with a multiplication to form a unital operator algebra, based solely on its underlying complex structure.
Contribution
It introduces a holomorphic condition that is both necessary and sufficient for an operator space to be isomorphic to a unital operator algebra.
Findings
Holomorphic structure determines algebraic multiplicative properties.
Characterization applies to operator spaces supporting a compatible multiplication.
Provides a new criterion linking complex analysis and operator algebra theory.
Abstract
A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach spaces underlying the operator space.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Advanced Topics in Algebra