Related papers: Some Character Generating Functions on Banach Alge…

We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff…

We present a Lebesgue-type decomposition for a representable functional on a $^*$-algebra into absolutely continuous and singular parts with respect to an other. This generalizes the corresponding results of S. P. Gudder for unital Banach…

Let $T$ be a Banach algebra homomorphism from a Banach algebra $\mathcal B$ to a Banach algebra $\mathcal A$ with $\|T\|\leq 1$. Recently it has been obtained some results about Arens regularity and also various notions of amenability of…

In this thesis we explore the the possibility of characterising C* algebras by their (non-isometric) Banach algebra structure alone. We introduce a property of Banach algebras, the Total Reduction Property, and conjecture that a Banach…

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable…

Let $\bold{\Phi}=(\phi_n)$ be a Musielak-Orlicz function, $X$ be a real Banach space and $A$ be any infinite matrix. In this paper, a generalized vector-valued Musielak-Orlicz sequence space $l_{\bold {\Phi}}^{A}(X)$ is introduced. It is…

Let $A$ be a Banach algebra and $\phi\in \Delta(A)\cup\{0\}$. We say that $A$ is $\Delta$-weak $\phi$-amenable if there exists an $m\in A^{**}$ such that $m(\phi)=0$ and $m(\psi.a)=\psi(a)$ for each $\psi\in \Delta(A)$ and $a\in…

We consider a Banach algebra $A$ with the property that, roughly speaking, sufficiently many irreducible representations of $A$ on nontrivial Banach spaces do not vanish on all square zero elements. The class of Banach algebras with this…

Using functional calculi theory, we obtain several estimates for $\|\psi(A)g(A)\|$, where $\psi$ is a Bernstein function, $g$ is a bounded completely monotone function and $-A$ is the generator of a holomorphic $C_0$-semigroup on a Banach…

The Gleason-Kahane-\.Zelazko theorem states that a linear functional on a Banach algebra that is non-zero on invertible elements is necessarily a scalar multiple of a character. Recently this theorem has been extended to certain Banach…

Let G be a locally compact group, let $\Omega:G\times G\to \mathbb{C}^*$ be a 2-cocycle, and let $\Phi$ be a Young function. In this paper, we consider the Orlicz space $L^\Phi(G)$ and investigate its algebraic property under the twisted…

For a fixed C*-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an A-dynamical system is a triple (i,B,\alpha) where $\alpha$ is a *-endomorphism of a C*-algebra B, and i: A --> B is…

In a previous paper (Radial operators on polyanalytic weighted Bergman spaces, Bol. Soc. Mat. Mex. 27, 43), using disk polynomials as an orthonormal basis in the $n$-analytic weighted Bergman space, we showed that for every bounded radial…

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order…

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in…

Let $\mathfrak{C}$ be a class of finite combinatorial structures. The \textit{profile} of $\mathfrak{C}$ is the function $\varphi_{\mathfrak{C}}$ which counts, for every integer $n$, the number $\varphi_{\mathfrak{C}}(n)$ of members of…

We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization…

A family $A_\alpha$ of differential operators depending on a real parameter $\alpha\ge 0$ is considered. This family was suggested by Smilansky as a model of an irreversible quantum system. We find the absolutely continuous spectrum…

We examine the analyticity of the class of separable Banach spaces possessing the $\pi$-property, defined in terms of convergence along a filter. Our results establish that this class is $\Sigma^1_3$ whenever the underlying filter is…

Let $ A$ be a complex unital Banach algebra. An element $a \in A$ is said to be Hermitian, if $ \| \exp (ita) \| =1$ for all $t\in R$. In the case of the algebra of bounded linear operators in a Hilbert space this Hermitian property agrees…