On Character Amenability of Banach Algebras

Details On Character Amenability of Banach Algebras On Character Amenability of Banach Algebras

2007-12-13

arxiv.org/abs/0712.2072v2

Mathematics

Functional Analysis

Keywords: Banach algebra, topological center, amenability

Scientific paper

Associated to a nonzero homomorphism $\varphi$ of a Banach algebra $A$, we regard special functionals, say $m_\varphi$, on certain subspaces of $A^\ast$ which provide equivalent statements to the existence of a bounded right approximate identity in the corresponding maximal ideal in $A$. For instance, applying a fixed point theorem yields an equivalent statement to the existence of a $m_\varphi$ on $A^\ast$; and, in addition we expatiate the case that if a functional $m_\varphi$ is unique, then $m_\varphi$ belongs to the topological center of the bidual algebra $A^{\ast\ast}$. An example of a function algebra, surprisingly, contradicts a conjecture that a Banach algebra $A$ is amenable if $A$ is $\varphi$-amenable in every character $\varphi$ and if functionals $m_\varphi$ associated to the characters $\varphi$ are uniformly bounded. Aforementioned are also elaborated on the direct sum of two given Banach algebras.

Affiliated with

Also associated with

No associations

Rating

On Character Amenability of Banach Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Character Amenability of Banach Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Character Amenability of Banach Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-622564