We study weakly compact operators from a C∗-algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector measures with values in a locally convex space. Several results of Brooks, Sâıto and Wright are extended to this more general setting. Building on an approach due to Sâıto and Wright, we obtain our theorems on no...

An extension of the Helson-Edwards theorem for the group algebras to Banach modules over commutative Banach algebras is given. This extension can be viewed as a generalization of Liu-Rooij-Wang's result for Banach modules over the group algebras.

In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ , and {αt} a strongly continuous extension to L(M, τ ) of a semigroup of absolute contractions on L(M, τ ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and x ∈ L(M, τ ), the averages 1 T Z T 0 b(t)αt(x)dt converge bilateral almost uniform in L(M, τ ) as T ...

In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ , and {αt} a strongly continuous extension to L(M, τ ) of a semigroup of absolute contractions on L(M, τ ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and x ∈ L(M, τ ), the averages 1 T Z T 0 b(t)αt(x)dt converge bilateral almost uniform in L(M, τ ) as T ...

We prove that, in the class of commutative topological algebras with separately continuous multiplication, an element is permanently singular if and only if it is a topological divisor of zero. This extends the result given by R. Arens [1] for the Banach algebra case. We also give sufficient conditions for non-removability of ideals in commutative topological algebras with jointly continuous mu...

We consider semi-group BMO spaces associated with an arbitrary $\sigma$-finite von Neumann algebra $(\mathcal{M}, \varphi)$. prove that the row and column always admit a predual, extending results from finite case. Consequently, we can considered are Banach they interpolate $L_p$ as in commutative situation, namely $[\mathrm{BMO}(\mathcal{M}), L_p^\circ(\mathcal{M})]_{1/q} \approx L_{pq}^\circ(...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

We develop two topics in parallel and show their inter-relation. The first centers on the notion of a fractional-differentiable structure on a commutative or a non-commutative space. We call this study quantum harmonic analysis. The second concerns homotopy invariants for these spaces and is an aspect of non-commutative geometry. We study an algebra A, which will be a Banach algebra with unit, ...