Related papers: Weighted inversion of vector valued Dirichlet seri…

We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($\Gamma, D(\Gamma)$) is given by $\Gamma f =…

An element $g$ of a group is called {\em reversible} if it is conjugate in the group to its inverse. In this paper we review some results about the structure of groups involving the reversible elements and we pose some questions about…

We introduce the concept of an $E$-valued function algebra, a type of Banach algebra that consist of continuous $E$-valued functions on some compact Hausdorff space, where $E$ is a Banach algebra. We present some basic results about such…

We study linear and algebraic structures in sets of Dirichlet series with maximal Bohr's strip. More precisely, we consider a set $\mathscr M$ of Dirichlet series which are uniformly continuous on the right half plane and whose strip of…

Let $W_0(\mathbb R)$ be the Wiener Banach algebra of functions representable by the Fourier integrals of Lebesgue integrable functions. It is proven in the paper that, in particular, a trigonometric series $\sum\limits_{k=-\infty}^\infty…

In this paper, we define $A_{\vartheta _{1},\vartheta _{2}}^{p,1,q,r}\left(G\right) $ to be space of all functions in $\left( L_{\vartheta_{1}}^{p},\ell ^{1}\right) $ whose Fourier transforms belong to $\left( L_{\vartheta _{2}}^{q},\ell…

Let $\Lambda$ be an open set in Banach space $E$, $M(x)$ for $x\in \Lambda $ be a subspace in $E$, and $x_0$ be a point in $\Lambda $. We consider the family $\mathcal{F}=\{M(x):\forall x\in\Lambda\}$, but the dimension of $M(x)$ can be…

Every differential subalgebra of a unital $C^*$-algebra is spectrally invariant. We derive a quantitative version of this well-known fact and show that a minimal amount of smoothness, as given by a differential norm, already implies norm…

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…

In this article we introduce several new examples of Wiener pairs $\mathcal{A} \subseteq \mathcal{B}$, where $\mathcal{B} = \mathcal{B}(\ell^2(X;\mathcal{H}))$ is the Banach algebra of bounded operators acting on the Hilbert space-valued…

In an earlier paper, Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and…

We begin with (densely-defined) fractional linear transformations (FLT) on (some) Banach algebras and their relatives. This leads to Wedderburn's continued fractions (recursively-defined noncommutative polynomials) for any ring. Along the…

Let $G$ be a locally compact group and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of $BSE$- Banach algebras $A$, and the Banach algebras $L^{1}(G, A)$ are…

Our basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible. So $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be…

If $D:A \to X$ is a derivation from a Banach algebra to a contractive, Banach $A$-bimodule, then one can equip $X^{**}$ with an $A^{**}$-bimodule structure, such that the second transpose $D^{**}: A^{**} \to X^{**}$ is again a derivation.…

For a Banach algebra $A$, we say that an element $M$ in $A\otimes^\gamma A$ is a hyper-commutator if $(a\otimes 1)M=M(1\otimes a)$ for every $a\in A$. A diagonal for a Banach algebra is a hyper-commutator which its image under diagonal…

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…

Let $G$ be a 1-connected Banach-Lie group or, more generally, a BCH--Lie group. On the complex enveloping algebra $U_\C(\g)$ of its Lie algebra $\g$ we define the concept of an analytic functional and show that every positive analytic…

We give a self-contained proof of a recently established $\mathcal{B}(\mathcal{H})$-valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of $\mathcal{B}(\mathcal{H})$-valued matrices, whose operator norms of their…

A discrete group $\G$ is called rigidly symmetric if for every $C^*$-algebra $\A$ the projective tensor product $\ell^1(\G)\widehat\otimes\A$ is a symmetric Banach $^*$-algebra. For such a group we show that the twisted crossed product…