Sets of periods for chaotic linear operators

POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

Partially continuous pretopological and topological operators for intuitionistic fuzzy sets

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

A geometric construction for fractal sets and related linear operators

Random sets of isomorphism of linear operators on Hilbert space

Abstract: This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator T on a Hilbert space with an orthogonal basis, we define the isomorphic structure Σ(T ) as the family of all subsets of the basis so that T restricted to their span is a nice isomorphism. Our main result is a dimension-free optimal estimate of the size of Σ(T ). It improve...

Approximation of Chaotic Operators

As well-known, the concept "hypercyclic" in operator theory is the same as the concept "transitive" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we consider classes of operators with some kinds of chaotic properties in this article. First of all, the closures of the sets of all Li-Yorke chaotic operators or...