Related papers: On the structure of Banach algebras associated wit…

We look for an effective description of the algebra D_{Lie}(X,B) of operators on a bimodule X over an algebra B, generated by inner derivations. It is shown that in some important examples D_{Lie}(X,B) consists of all elementary operators…

We define reduced and essential Banach algebras associated to a twisted \'{e}tale (not necessarily Hausdorff) groupoid $(\mathcal{G},\mathcal{L})$ and extend some fundamental results from $C^*$-algebras to this context. We prove that for…

We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of…

Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such…

We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach…

In this paper, we introduce a notion of geometric Banach property (T) for metric spaces, which jointly generalizes Banach property (T) for groups and geometric property (T) for metric spaces. Our framework is achieved by Banach…

Let $A$ be a Banach algebra, not necessarily unital, and let $B$ be a closed subalgebra of $A$. We establish a connection between the Banach cyclic cohomology group $ {\cal{HC}}^n(A)$ of $A$ and the Banach $B$-relative cyclic cohomology…

We investigate the structure of the free $p$-convex Banach lattice $FBL^{(p)}[E]$ over a Banach space $E$. After recalling why such a free lattice exists, and giving a convenient functional representation of it, we focus our study on how…

Let $B$ be a Banach $A-bimodule$ and let $n\geq 0$. We investigate the relationships between some cohomological groups of $A$, that is, if the topological center of the left module action $\pi_\ell:A\times B\rightarrow B$ of $A^{(2n)}$ on…

Let G be a locally compact group. We use the canonical operator space structure on the spaces $L^p(G)$ for $p \in [1,\infty]$ introduced by G. Pisier to define operator space analogues $OA_p(G)$ of the classical Figa-Talamanca-Herz algebras…

Recently Pascal Baseilhac and Stefan Kolb introduced some automorphisms $T_0$, $T_1$ of the $q$-Onsager algebra $\mathcal O_q$, that are roughly analogous to the Lusztig automorphisms of $U_q(\widehat{\mathfrak{sl}}_2)$. We use $T_0, T_1$…

In this paper, first we study some Arens regularity properties of module actions. Let $B$ be a Banach $A-bimodule$ and let ${Z}^\ell_{B^{**}}(A^{**})$ and ${Z}^\ell_{A^{**}}(B^{**})$ be the topological centers of the left module action…

We characterize boundedness and compactness of the classical Volterra operator $T_g \colon H_{v_{\alpha}}^{\infty} \to H^{\infty}$ induced by a univalent function $g$ for standard weights $v_{\alpha}$ with $0 \leq \alpha < 1$, partly…

In this paper, we observe the amalgamated free product structure of a Graph W*-probability space. In [16] and [17], we already observed the operator-valued freeness conditions on a graph W*-algebra. By using the conditions, we will consider…

By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group $\mathbb{G}$ a completely contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a deformed Fourier…

We construct an explicit transitive free action of a Banach space of H\"older functions on the space of branched rough paths, which yields in particular a bijection between theses two spaces. This endows the space of branched rough paths…

We investigate the action of Schur algebra on the Lie algebras of derivations of free Lie algebras and operad structures constructed from it. We also show that the Lie algebra of derivations is generated by quadratic derivations together…

Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors…

In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of…

In the present note we introduce tame functionals on Banach algebras. A functional $f \in A^*$ on a Banach algebra $A$ is tame if the naturally defined linear operator $A \to A^*, a \mapsto f \cdot a$ factors through Rosenthal Banach spaces…