Title: Operator Algebras with Contractive Approximate Identities
Abstract:Abstract We study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L ∞ - Banach algebras with contractiv...Abstract We study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L ∞ - Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M ( A ) may admit different operator algebra matrix norms, with which M ( A ) contains A as an M -ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A 1 of A such that A 1 contains A as an M -ideal.Read More