Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

There has been a growing interest in the study of the notion of $alpha$-migrativity and generalizations in recent years, and it has been investigated for families of certain operators such as t-norms, t-conorms, uninorms, nullnorms.This paper is mainly devoted to investigating the migrativity equations between semi-t-operators or semi-uninorms, and Mayor's aggregation operators. The results tha...

We extend the recent stability results of Ambrozie for Fredholm essential complexes to the semi-Fredholm case. Let X,Y be Banach spaces. By an operator we always mean a bounded linear operator. The set of all operators from X to Y will be denoted by L(X,Y ). Denote by N(T ) and R(T ) the kernel and range of an operator T ∈ L(X, Y ). Recall that an operator T : X → Y is called semi-Fredholm if i...

An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators. Denote by L(X) the algebra of all bounded linear operators i...

The conditional distributivity, that is distributivity equation with additional restriction imposed on the domain of aggregation operations, an issue interest for many different theoretical and practical areas, special integration theory utility theory. This paper presents new results this specific form semi-t-operators over conjunctive uninorms. Since observed class uninorms rather wide includ...

Uninorms introduced by Yager in 1996 are a new class of aggregation operators, which are also an important generalization of t-norms and t-conorms. At present, uninorms have been widely used in lots of fields such as expert system, decision making, fuzzy reasoning, image processing and so on. In the theoretical study about this class of operators, several subclasses emerged, and some extensions...

The aim of this paper was to introduce and investigate a new seminorm operator tuples on complex Hilbert space H when an additional semi-inner product structure defined by positive (semi-definite) A is considered. We prove the equality between well-known A-joint in case A-doubly-commuting A-hyponormal operators. This study extension result [Results Math 75, 93(2020)] allows us show that followi...

In this paper we characterize when the semi-commutator TfTg − Tfg of two Toeplitz operators Tf and Tg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T 2 are given.