Related papers: Interpolating sequences for the Banach algebras ge…

We prove that the crossed product Banach algebra $\ell^1(A,G,\alpha)$ that is associated with a $\mathrm{C}^\ast$-dynamical system $(A,G,\alpha)$ is amenable if $G$ is a discrete amenable group and $A$ is a commutative or finite dimensional…

We introduce Banach algebras associated to twisted \'etale groupoids $(\mathcal{G},\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the…

In this paper, among other things, we study those conditions under which the weighted semigroup algebra $\ell^1(S,\omega)$ is a dual Banach algebra with respect to predual $c_0(S)$. Some useful examples, illustrating the results, are also…

In [3] S. J. Bhatt and H. V. Dedania exposed certain classes of Banach algebras in which every element is a topological divisor of zero. We identify a new (large) class of Banach algebras with the aforementioned property, namely, the class…

In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a…

Characterization of Schur-class functions (analytic and bounded by one in modulus on the open unit disk) in terms of their Taylor coefficients at the origin is due to I. Schur. We present a boundary analog of this result: necessary and…

We investigate the stability of compactness of bilinear operators acting on the product of interpolation of Banach spaces. We develop a general framework for such results and our method applies to abstract methods of interpolation in the…

In this article, we attempt to introduce the "Multiplier algebra" associated to the Fock representation that arising from the left-cancellative semigroup $\mathcal{S}$ (denoted by $M(\mathcal{S})$) by adopting the concept of multiplier…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…

The paper studies projective freeness and Hermiteness of algebras of complex-valued continuous functions on topological spaces, Stein algebras, and commutative unital Banach algebras. New sufficient cohomology conditions on the maximal…

The manifold structure of subsets of classical probability distributions and quantum density operators in infinite dimensions is investigated in the context of $C^{*}$-algebras and actions of Banach-Lie groups. Specificaly, classical…

The Schur-Agler class consists of functions over a domain satisfying an appropriate von Neumann inequality. Originally defined over the polydisk, the idea has been extended to general domains in multivariable complex Euclidean space with…

Let $X(\mathbb{Z})$ be a reflexive rearrangement-invariant Banach sequence space with nontrivial Boyd indices $\alpha_X,\beta_X$ and let $w$ be a symmetric weight in the intersection of the Muckenhoupt classes $A_{1/\alpha_X}(\mathbb{Z})$…

In this paper we study two types of collections of operators on a Banach space on the subject of forming operator ideals. One of the types allows us to construct an uncountable chain of closed ideals in each of the operator algebras…

Let $({\sf G},\alpha, \omega,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is…

We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator…

The proofs of A. Villani on inclusion relations among classical Lebesgue spaces are dicussed. The techinque of using closed graph theorem, due to Villani, is applied to derive results on inclusion relations among some more additional…

As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there…

Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences…

We introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the…