# Tagged Questions

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### On existence of right units with control of their norms

Does, there exist a Banach algebra with a family of right units with norms converging to 1, but without right unit of norm 1?
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### On $C_0(\Omega)$-module maps from $L_\infty(\Omega,\mu)$ to $L_q(\Omega,\nu)$

Let $\Omega$ be a locally compact space, and $\mu,\nu\in C_0(\Omega)^*$. By $H_{p,q}^{B}$ (resp. $H_{p,q}^{C}$) we denote the Banach space of continuous $B(\Omega)$-module (resp. $C_0(\Omega)$-module) ...
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### Specific Reference? Noncommutative topology and C^* algebras [closed]

I stumbled across this "dictionary for noncommutative topology" http://planetmath.org/noncommutativetopology and I would be very interested in learning more on the subject, particularly I'd like to ...
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### $L^{p}(\mathbb R)\subset L^{1}(\mathbb R) \ast L^{p}(\mathbb R), (1< p< \infty)$?

Let $\mathbb T$ be a circle group. In 1939, Salem, has shown that, every member of $L^{1}(\mathbb T)$ can written as a product(convolution) some other two members of $L^{1}(\mathbb T),$ that is, ...
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### Regular commutative Banach algebras which are not closed under complex conjugate

Let $A$ be a semisimple commutative Banach algebra with the maximal ideal space $X$. Further, assume that $A$ is regular i.e. for every closed set $E\subseteq X$ and $x\in X\setminus E$, there is some ...
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### Existence of certain bounded approximate identity

In trying to follow the proof of Proposition 4.11 in M. C. White, Injective modules for uniform algebras, Proc. London Math. Soc. 73 (1996) 155--184 there is a part which seems unclear. Let $I$ be ...
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### Banach Algebra Counterexample

Can someone give me an example of a Banach Algebra which does not have an isometric representation in a Hilbert Space ? (if possible, can you add a proof or a reference ? ) Thank you very much ! ...
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### On hyperplanes of $L\infty$

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 there "natural" ...
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### Maximal spectrum of a complex, unital and commutative Banach-algebra

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 $Spec(A)$ of $A$, Hausdorff? ...
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### Subalgebras of $B(E)$

Let me fix an infinite-dimensional (complex) Banach space $E$. There is a cute result of Bracic and Kuzma which says that every maximal abelian subalgebra of $\mathscr{B}(E)$, the algebra of bounded ...
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### Tensorial decomposition of $B(H)$

Let $H$ be an infinite-dimensional Hilbert space and let $\mathcal{B}(H)$ be the (C*/W*-)algebra of bounded operators on it. Actually, you may forget about the involution in $\mathcal{B}(H)$ because I ...
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### Banach Algebras and the peripheral spectrum

Here is a little theorem that I'm trying to prove. I haven't seen it in literature before, but I think the applications will be quite useful, particularly in the context of Banach algebras. Denote ...
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### When is a Banach Algebra $C^\star$

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 $B(L^1(S^1,\Sigma,\mu))$ the space of ...
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### Injective modules over Fourier algebra

Is there any article on injective modules over Fourier Algebras? Do we have anything about injectivity of $A(G)$ as a $A(G)$-bimodule?