# Tagged Questions

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146 views

### A certain measure on Banach algebras

According to the comments of Nate Eldredge I did revise the question. In particular I change "$C^{*}$ algebras" to "Banach algebras". Is there a reference who introduce the following measure on ...
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### is every element in a C* algebra a product of normal elements?

I have the following question and since I am not an expert on C*-algebras, I thought I ask it here: I know that in general the sum and product of normal elements need not be normal. It is even true ...
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### $p$-operator space structure on Banach algebras

There is an abstract characterization of operator algebras, which says that if $A$ is an operator space that is also an approximately unital Banach algebra, then the following are equivalent: For ...
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### $C[0,1]$ is Banach-space isomorphic to $c_0(C[0,1])$

$c_0(C[0,1])$ is the $c_0$-direct sum of countably many $C[0,1]$.How to prove $C[0,1]$ is Banach-space isomorphic to $c_0(C[0,1])$. Here,Banach-space isomorphism means a bounded invertible operator ...
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### Can we obtain a derived category from an additive category? Like a category of Banach modules?

Let $A$ be a Banach algebra, let $A$-mod be the category of left Banach modules (as defined in Helemskii's "Banach and locally convex algebras"), $A$-mod is an additive category, but not abelian ...
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### Can we extend a multiplicative linear functional of a closed left ideal on whole of the algebra?

Let B be a closed left ideal of a Banach algebra A. Also, B has a right approximate identity (in B). If g is a nonzero multiplicative linear functional on B, can we always extend g to a ...
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### Is $\mathcal{K}(H)$ injective $\mathcal{B}(H)$-module?

Does anyone know if the right Banach $\mathcal{B}(H)$-module $\mathcal{K}(H)$ is injective? The same question for $\ell_\infty$-module $c_0$. Both these modules are not dual, so standard arguments ...
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### Are norm-continuous representations smooth?

Let $G$ be a real Lie group and $A$ a unital Banach algebra. Let us call a map $\varphi:G\to A$ a (norm-)continuous representation, if it is continuous  x_i\to x\quad\Longrightarrow\quad ||\varphi(...
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### A commutative Banach algebra with an abundance of discountinuous functions

Let $A$ be the algebra of all bounded functions from $[0,\;1]$ to $\mathbb{C}$. For $f\in A,\;$ $\omega_{f}$ is the standard oscillation function.. Each of the following two (equivalent) norms ...
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### When $C(X)$ is an injective $C(X)$-module? Current answer is erroneous

It is an old question if every injective Banach space is isomorphic as Banach space to $C(X)$-space. I would like to know if the weakened module version of this question is answered. More precisely: ...
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### C*-Algebras: Dynamics vs. Derivations

Problem Given a C*-algebra $\mathcal{A}$. Consider dynamics $\tau:\mathbb{R}\to\mathrm{Aut}(\mathcal{A})$ and $\tau':\mathbb{R}\to\mathrm{Aut}(\mathcal{A})$. (More precisely, strongly continuous one-...
Let $A$ be a unital Banach algebra, $U$ be an open subset of $\mathbb{C}$, and $A_U:=\{x\in A:\sigma(x)\subset U\}$. Holomorphic functional calculus says that any holomorphic function $f:U\rightarrow\... 1answer 252 views ### Non commutative topological manifolds Assume that$A$is a Banach algebra with two closed two sided ideals$I$and$J$such that$I$and$J$are commutative and$A=I+J$. Does this implies that$A$is commutative? For the$C^{*...
Let $G$ be a locally compact SIN-group. Then $ZL^{1}(G)$ has a bounded approximate identity. I want to prove that the multiplier algebra of $ZL^{1}(G)$ is equal to $ZM(G)$ (center of measure algebra). ...