On Character Amenability of Banach Algebras
Ahmadreza Azimifard

TL;DR
This paper explores the concept of character amenability in Banach algebras, linking it to special functionals, approximate identities, and topological centers, with examples challenging existing conjectures.
Contribution
It introduces new characterizations of character amenability using special functionals and provides counterexamples to a conjecture relating amenability and $ extit{ ext{φ}}$-amenability.
Findings
Existence of special functionals $m_ extit{ ext{φ}}$ relates to approximate identities.
Unique $m_ extit{ ext{φ}}$ belongs to the topological center of $A^{**}$.
An example contradicts the conjecture that $ extit{ ext{φ}}$-amenability implies amenability.
Abstract
Associated to a nonzero homomorphism of a Banach algebra , we regard special functionals, say , on certain subspaces of which provide equivalent statements to the existence of a bounded right approximate identity in the corresponding maximal ideal in . For instance, applying a fixed point theorem yields an equivalent statement to the existence of a on ; and, in addition we expatiate the case that if a functional is unique, then belongs to the topological center of the bidual algebra . An example of a function algebra, surprisingly, contradicts a conjecture that a Banach algebra is amenable if is -amenable in every character and if functionals associated to the characters are uniformly bounded. Aforementioned are also elaborated on the direct sum…
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Topics in Algebra
