Related papers: Weakly almost periodic functionals on the measure …

In this paper, we study the weak amenability of weighted measure algebras and prove that $M(G, \omega)$ is weakly amenable if and only if $G$ is discrete and every bounded quasi-additive function is inner. We also study the weak amenability…

A weak multiplier Hopf algebra is a pair (A,\Delta) of a non-degenerate idempotent algebra A and a coproduct $\Delta$ on A. The coproduct is a coassociative homomorphism from A to the multiplier algebra M(A\otimes A) with some natural extra…

We characterise the strictly closed left invariant C*-subalgebras of the C*-algebra C_b(G) of bounded continuous functions on a locally compact group G. On the dual side, we characterise the strictly closed invariant C*-subalgebras of the…

We give a detailed comparison between the notion of a weak Hopf algebra (also called a quantum groupoid by Nikshych and Vainerman), and that of a $\times_R$-bialgebra due to Takeuchi (and also called a bialgebroid or quantum (semi)groupoid…

We initiate the study of pointed approximative absolute neighborhood retracts. Our motivation is to generate examples of C*-algebras that behave in unexpected ways with respect to weak semiprojectivity. We consider both weak…

A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…

We consider an action of the circle group, T on a von Neumann algebra, M. Similarly to the case when the algebra of essentially bounded functions on T is acted upon by translations, we define the generalized Hardy subspace of H,where H is…

In this paper we investigate Hartman functions on a topological group $G$. Recall that $(\iota, C)$ is a group compactification of $G$ if $C$ is a compact group, $\iota: G\to C$ is a continuous group homomorphism and $\iota(G)$ is dense in…

Via Gelfand duality, a unital C*-algebra $A$ induces a functor from compact Hausdorff spaces to sets, $\mathsf{CHaus}\to\mathsf{Set}$. We show how this functor encodes standard functional calculus in $A$ as well as its multivariate…

A theorem of Siebert asserts that if a sequence of semigroups of probability measures on a Lie group G is weakly convergent to a semigroup of the same type, then the corresponding generating functionals are convergent in the weak operator…

A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…

We study operator algebraic and function theoretic aspects of algebras of bounded nc functions on subvarieties of the nc domain determined by all levels of the unit ball of an operator space (nc operator balls). Our main result is the…

Let $M$ be a finite von Neumann algebra. In the first part, we give asymptotic results about $M$-stable sequences of weak*-continuous mappings which are related with operators belonging to $M$. In the second part, we extend, by a shorter…

We investigate possible preduals of the measure algebra $M(G)$ of a locally compact group and the Fourier algebra $A(G)$ of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the…

We analyze semigroups of decomposable maps on C*-algebras in context of the algebraic structure of associated infinitesimal generators. Case of von Neumann algebras, including $B(\mathcal{H})$ for $\mathcal{H}$ a Hilbert space, is also…

In this series of papers, we develop the theory of a class of locally compact quantum groupoids, which is motivated by the purely algebraic notion of weak multiplier Hopf algebras. In this Part I, we provide motivation and formulate the…

The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an important role in several subfields of…

We show that every Finsler module over a $C^*$-algebra has a quasi-representation into the Banach space $\mathbb{B}(\mathscr{H},\mathscr{K})$ of all bounded linear operators between some Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$. We…

In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra $\mathcal{T}$. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual…

An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property;…