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Search: All articles in the CMB digital archive with keyword Banach algebras

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1. CMB Online first

Alaghmandan, Mahmod
Approximate amenability of Segal algebras II
We prove that every proper Segal algebra of a SIN group is not approximately amenable.

Keywords:Segal algebras, approximate amenability, SIN groups, commutative Banach algebras
Categories:46H20, 43A20

2. CMB Online first

Alaghmandan, Mahmod
Approximate amenability of Segal algebras II
We prove that every proper Segal algebra of a SIN group is not approximately amenable.

Keywords:Segal algebras, approximate amenability, SIN groups, commutative Banach algebras
Categories:46H20, 43A20

3. CMB 2012 (vol 56 pp. 534)

Filali, M.; Monfared, M. Sangani
A Cohomological Property of $\pi$-invariant Elements
Let $A$ be a Banach algebra and $\pi \colon A \longrightarrow \mathscr L(H)$ be a continuous representation of $A$ on a separable Hilbert space $H$ with $\dim H =\frak m$. Let $\pi_{ij}$ be the coordinate functions of $\pi$ with respect to an orthonormal basis and suppose that for each $1\le j \le \frak m$, $C_j=\sum_{i=1}^{\frak m} \|\pi_{ij}\|_{A^*}\lt \infty$ and $\sup_j C_j\lt \infty$. Under these conditions, we call an element $\overline\Phi \in l^\infty (\frak m , A^{**})$ left $\pi$-invariant if $a\cdot \overline\Phi ={}^t\pi (a) \overline\Phi$ for all $a\in A$. In this paper we prove a link between the existence of left $\pi$-invariant elements and the vanishing of certain Hochschild cohomology groups of $A$. Our results extend an earlier result by Lau on $F$-algebras and recent results of Kaniuth-Lau-Pym and the second named author in the special case that $\pi \colon A \longrightarrow \mathbf C$ is a non-zero character on $A$.

Keywords:Banach algebras, $\pi$-invariance, derivations, representations
Categories:46H15, 46H25, 13N15

4. CMB 2009 (vol 53 pp. 51)

Cobos, Fernando; Fernández-Cabrera, Luz M.
On the Relationship Between Interpolation of Banach Algebras and Interpolation of Bilinear Operators
We show that if the general real method $(\cdot ,\cdot )_\Gamma$ preserves the Banach-algebra structure, then a bilinear interpolation theorem holds for $(\cdot ,\cdot )_\Gamma$.

Keywords:real interpolation, bilinear operators, Banach algebras
Categories:46B70, 46M35, 46H05

5. CMB 2003 (vol 46 pp. 632)

Runde, Volker
The Operator Amenability of Uniform Algebras
We prove a quantized version of a theorem by M.~V.~She\u{\i}nberg: A uniform algebra equipped with its canonical, {\it i.e.}, minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.

Keywords:uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space
Categories:46H20, 46H25, 46J10, 46J40, 47L25

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