We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent associated with rational function. also study connections to Cuntz relations. An important tool new representation result for analytic functions, in terms of composition and multiplication operators given Applications theory de Branges-Rovnyak spaces, indefinite metric sett...

The aim of this paper is to answer the following question concerning invariant subspaces composition operators: characterize ?, holomorphic self maps D, and inner functions ??H?(D) such that Beurling type subspace ?H2 an for C?. We prove result: C?(?H2)??H2 if only ?????S(D). This classification also allows us recover or improve some known results on operators.

We prove that RS-BL-algebras are MV-algebras.

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...