Let $\mathbb{T}=[0,1]$ be identified with the circle $\{ e^{2 \pi it} : t \in [0,1] \}$, $\delta_0 \in M(\mathbb{T})$ be the Dirac measure at $0 \in \mathbb{T}$. Suppose $f \in L^1 …

Hello 1)IS ANY relationship between character amenability and weak amenability of Banach algebras?.... If a Banach $A$ is amenable then $A$ is $\phi$-amenable for every $\phi\i …

Let $\cal A$ be a weak amenable Banach algebra and $T:\cal A \to \cal B$ be a surjective homomorphism ($\cal B$ is a Banach algebra). Dose ker(T) has the trace extention property i …

Consider the hyperplane $H=\{f\in L^\infty: \int f = 0\}$ of $L^\infty = L^\infty[0,1]$. My question is: 1. What is the Banach-Mazur distance between $H$ and $L^\infty$? Are ther …

Let $A$ be a $C^*\text{-algbera}$ and $x\in A$ i'm trying to show thata)for $0<\alpha<\frac{1}{2}$, there exists $u\in A$ with $x=u(x^*x)^{\alpha}$ and $u^*u=(x^*x)^{1-2\alph …

Lel $B$ be a Banach algebra and give $B^{**}$ one of the Arens products in order to make it a Banach algebra. Then the canonical embedding $\kappa\colon B\to B^{\ast\ast}$ is a hom …

If an algebra $A$ is a semidirect product of a subalgebra $B$ and an ideal $I$. Is characterized the character space of $A$ by character space of $B$ and character space of $I$?

This problem was posed on Math StackExchange some time ago, but it did not garner any solutions there. I think that it is interesting enough to be posed here on Math Overflow, so h …

Dear All, I am absolutely lost in the following problem: Let $P_s, \: s \in [0,1],$ be a uniformly bounded family of projections (idempotents) in a Banach space $X$ such that $P …

A real function $f:X\rightarrow \mathbb{R}$ Is called Baire-one function, if there is a sequence $(f_n)_{n=1} ^\infty$ of continuous functions $f_n:X\rightarrow \mathbb{R}$ on $X$ …

Let $A$ be a complex, unital and commutative Banach-algebra. Question: Is the maximal spectrum $Max(A)$ of $A$ endowed with the topology induced by the prime spectrum $Spec(A)$ o …

I know that if there are enough Hermitian elements in a Banach algebra, then the Banach algebra is stellar. In particular, I'm interested in the two spaces $B(L^1(S^1,\Sigma,\mu))$ …

This is admittedly a low-interest question mathematically, and is arguably a question I could resolve if I had time over the next few days to go and look through a large number of …

I am interested in operators on a non-reflexive Banach space. Let $X$ be a Banach space and let $L(X)$ be the algebra of operators acting on $X$. We may embed $L(X)$ into $L(X^{\as …

I am interested in the group algebras of non-locally compact groups. What references can you advise? This is a wide question, so I list more concretely what I would like to see: …