Convolution and separate continuity

Continuity of convolution and SIN groups

Let the measure algebra of a topological group G be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if G has the SIN property. On the space LUC(G)∗ which includes the measure algebra, convolution is also jointly continuous if and on...

Separate and Joint Continuity of Homomorphisms Defined on Topological Groups

In this paper we prove the following theorem. “Let H be a countably Čech–complete topological group, X be a topological space and (G, ·, τ) be a topological group. If f : H ×X → G is a separately continuous mapping with the property that for each x ∈ X, the mapping h 7→ f(h, x) is a group homomorphism, then for each q–point x0 ∈ X the mapping f is jointly continuous at each point of H ×{x0}.” W...

Convolution and Homogeneous Spaces

Non-commutative separate continuity and weakly almost periodicity for Hopf von Neumann algebras

For a compact Hausdorff space X , the space SC(X ×X) of separately continuous complex valued functions on X can be viewed as a C∗-subalgebra of C(X)∗∗⊗C(X)∗∗, namely those elements which slice into C(X). The analogous definition for a non-commutative C∗-algebra does not necessarily give an algebra, but we show that there is always a greatest C∗-subalgebra. This thus gives a noncommutative notio...

On the Theorems of Y . Mibu and G . Debs on Separate Continuity

Using a game-theoretic characterization of Baire spaces, conditions upon the domain and the range are given to ensure a "fat" set C(f) of points of continuity in the sets of type X x {/}, y E Y for certain almost separately continuous functions f X Y Z These results (especially Theorem B) generalize Mibu’s First Theorem, previous theorems of the author, answers one of his problems as well as th...