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.

In this paper the idea of -locally closed sets in generalized topological space is introduced and study some of their properties. We introduce the notion of (,’)locally closed continuous functions on generalized topological space and investigate some of their characterizations.

The paper considers the role of quantale algebra nuclei in representation of quotients of quantale algebras, and in factorization of quantale algebra homomorphisms. The set of all nuclei on a given quantale algebra is endowed with the structure of quantale semi-algebra.

In this paper, we first discuss the structure of the Ramond N = 2 superconformal algebras. Then we classify the modules of the intermediate series over Ramond N = 2 superconformal algebra.

We investigate the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal-free cylindric algebras. We prove that a Df2algebra is finitely representable iff it is finitely approximable, characterize finite projective Df2-algebras, and show that there are no non-trivial injectives and absolute retracts in Df2. We prove that every proper subvariety of Df2 is locally fini...

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 introduce a notion of “hopfish algebra” structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras are examples of hopfish algebras. We find that a hopfish structure on the algebra of functions on a finite set G is closely related to a “hypergroupoid” structure on G. ...

Some simple Lie superalgebras, specific of characteristic 3, defined by S. Bouarroudj and D. Leites [BL06], will be related to the simple alternative and commutative superalgebras discovered by I.P. Shestakov [She97]. Throughout the paper, the ground field k will always be assumed to be of characteristic 6= 2. 1. Tits construction In 1966 [Tit66], Tits gave a unified construction of the excepti...