Related papers: Arens Regularity And Factorization Property

Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollob\'as proved the nowadays known as the Bishop-Phelps-Bollob\'as theorem, which…

Let $M(S)$ be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup $S$ with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for…

Let G be an infinite discrete group and bG its Cech-Stone compactification. Using the well known fact that a free ultrafilter on an infinite set is nonmeasurable, we show that for each element p of the remainder bG G, left multiplication…

Let $A$ be a dual Banach algebra with predual $A_\ast$ and consider the following assertions: (A) $A$ is Connes-amenable; (B) $A$ has a normal, virtual diagonal; (C) $A_\ast$ is an injective $A$-bimodule. For general $A$, all that is known…

We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak…

The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a much simpler form. In this paper we provide simple…

Supppose given a principal $G$ bundle $\zeta : P \to S^k$ (with $k \geq 2$) and a Banach algebra $B$ upon which $G$ acts continuously. Let \[ \zeta\otimes B : \qquad P \times_G B \longrightarrow S^k \] denote the associated bundle and let…

In this article, we study the so-called abelian Rokhlin property for actions of locally compact, abelian groups on C$^*$-algebras. We propose a unifying framework for obtaining various duality results related to this property. The abelian…

In this article, we study the permanence of topological and algebraic dimension type properties of simple unital $C\sp*$-algebras. When a pair of unital $C\sp*$-algebras $(A, B)$ is associated by a $*$-homomorphism $\phi: A\to B$ which is…

The subject of this thesis is the modular group of automorphisms acting on the massive algebra of local observables having their support in bounded open subsets of Minkowski space. After a compact introduction to micro-local analysis and…

Given an action $G \curvearrowright X$ of a discrete and countable infinite group $G$ on a compact and Hausdorff space $X$, we regard $\ell^1(G\curvearrowright X)$ as the Banach *-algebra crossed product associated to the action. We…

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…

Let $R$ be a commutative ring and $M$ an $R$-module. Let $Spec^s(M)$ be the the collection of all second submodules of $M$. In this article, we consider a new topology on $Spec^s(M)$, called the second classical Zariski topology, and…

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…

Let $M$ be a non-zero module over an associative (not necessarily commutative) ring. In this paper, we investigate the so-called \emph{second} and \emph{coprime} submodules of $M.$ Moreover, we topologize the spectrum $%…

We study actions of discrete groups on Hilbert $C^*$-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a…

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, e.g., as lengths of catheti of right-angled triangles (defined via so-called quasi-orthogonality). These…

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…

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly outer $*$-automorphisms. In this paper we study the containment $M \subseteq M\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize the intermediate…

Let G be a locally compact group and let $A_\Phi(G)$ be the Orlicz-version of the Fig\`{a}-Talamanca Herz algebra of G associated with a Young function $\Phi.$ We show that if $A_\Phi(G)$ is Arens regular, then $G$ is discrete. We further…