Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences ConA. Mal’cev properties of V influence the structure of Unif A, much the same as they do that of ConA. The category V[CHUnif] of complete, Hausdorff unifor...

We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other. [MSC: 46J05, 46J10]

We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis opertors or weakly compact operators, on some uniform algebras of analytic functions. Even in the frame of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence of a general study of weighted composition operators.

All seven intermediate logics admitting Craig interpolation also admit uniform interpolation; however, although the modal logic K admits both properties, its extension S4 admits only Craig interpolation and not uniform interpolation (see [1] for details and references). Uniform interpolation for a logic may be viewed as a weaker form of quantifier elimination. This idea is exploited in the mono...

Although derivations from Banach algebras to particular coefficient modules have been much studied, interest has usually focused on the existence or otherwise of non-trivial bounded derivations, rather than their characterisation. Even in the special case of derivations from a commutative Banach algebra to its dual (as in [2] or [5] for example), there are comparatively few examples where the s...

In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$,  where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T...