Related papers: Arens regularity of projective tensor products

Let WAP(A) be the space of all weakly almost periodic functionals on a Banach algebra A. The Banach algebra A for which the natural embedding of A into WAP(A)* is bounded below is called a WAP-algebra. We show that the second dual of a…

We show that a continuously-normed Banach bundle $\mathcal{E}$ over a compact Hausdorff space $X$ whose space of sections is algebraically finitely-generated (f.g.) over $C(X)$ is locally trivial (and hence the section space is projective…

Let $E_1, \ldots, E_m$ be (non necessarily Archimedean) Riesz spaces, let $F$ be an Archimedean Riesz space and let $A \colon E_1 \times \cdots \times E_m \to F$ be a regular disjointness preserving $m$-linear operator. We prove that all…

We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous…

The purpose of this note is to show that, if $\mcB$ is a uniformly convex Banach, then the dual space $\mcB'$ has a "Hilbert space representation" (defined in the paper), that makes $\mcB$ much closer to a Hilbert space then previously…

We introduce a norm-controlled notion of semiprojectivity for Banach lattices, requiring liftability of contractive lattice homomorphisms through inductive limits of closed ideals with arbitrarily small loss of norm control. Our main result…

We investigate the higher-dimensional amenability of tensor products $\A \ptp \B$ of Banach algebras $\A$ and $\B$. We prove that the weak bidimension $db_w$ of the tensor product $\A \ptp \B$ of Banach algebras $\A$ and $\B$ with bounded…

Let $1 \in A \subset B$ be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of $B$ ($= \tsr(B)$) when $A$ has topological stable rank one. We show that $\tsr(B) \leq 2$ when $A$ is…

We give a description of operator algebras of free wreath products in terms of fundamental algebras of graphs of operator algebras as well as an explicit formula for the Haar state. This allows us to deduce stability properties for certain…

Let $A$ and $B$ be Banach algebras and let $T$ be an algebra homomorphism from $B$ into $A$. The Cartesian product space $A\times B$ by $T$- Lau product and $\ell^{1}$- norm becomes a Banach algebra $A\times_{T}B$. We investigate the…

It is well known that the bidual of $\mathrm C(X)$ for a compact space $X$, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)$ for some compact space $\tilde X$. The space $\tilde X$ is…

We study the smoothness and the norm attainment of bounded bilinear operators between Banach spaces, using the concepts of Birkhoff-James orthogonality and semi-inner-products. In the finite-dimensional case, we characterize Birkhoff-James…

This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field k. The main result establishes necessary and sufficient conditions for a Noetherian tensor product of two extension fields of k…

Let $(G, P)$ be an abelian, lattice ordered group and let $X$ be a compactly aligned product system over $P$. We show that the C*-envelope of the Nica tensor algebra $\mathcal{N}\mathcal{T}^+_X$ coincides with both Sehnem's covariance…

Let $G$ be a locally compact group, $A_p (G)$ be the Herz algebra of $G$ associated with $1 <p< \infty$. We show that $A_p (G)$ is Arens regular if and only if $G$ is a discrete group and for each countable subgroup $H$ of $G$, $A_p (H)$ is…

We consider several notions of regularity, including strong regularity, bounded relative units, and Ditkin's condition, in the setting of vector-valued function algebras. Given a commutative Banach algebra $A$ and a compact space $X$, let…

Recently, E.\ Kirchberg [K1--2] revived the study of pairs of $C^*$-algebras $A,B$ such that there is only one $C^*$-norm on the algebraic tensor product $A\otimes B$, or equivalently such that $A \otimes_{\rm min}B = A\otimes_{\rm max}B$.…

The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if $X\hat{\otimes}_\pi Y$ is strongly subdifferentiable and either $X$ or $Y$ has the metric…

Let $X$ be a compact metric space, let $A$ be a unital AH algebra with large matrix sizes, and let $B$ be a stably finite unital C*-algebra. Then we give a lower bound for the radius of comparison of $C(X) \otimes B$ and prove that the…

Let F(X) denote the norm closure of the space of all finite rank operators on a Banach space X. We show that there are Banach spaces X for which the product map $a\otimes b\to ab$ does not define a surjective map from the projective tensor…