Quasi-contractivity, Stability and convergence of WCT operators

TL;DR

This paper characterizes quasi-contraction, stability, and convergence properties of weighted conditional type operators on L^p spaces, establishing equivalences among various stability notions and providing illustrative examples.

Contribution

It offers new characterizations of quasi-contraction WCT operators and proves the equivalence of different stability concepts for these operators.

Findings

Equivalent conditions for quasi-contraction WCT operators

Convergence and stability notions are equivalent for WCT operators

Provided concrete examples illustrating the theoretical results

Abstract

In this paper we characterize quasi-contraction, stable and convergent weighted conditional type (WCT) operators on $L^p(\mu)$. Indeed we provide equivalent conditions for quasi-contraction WCT operators. Also, we prove that convergence, uniformly stability, strongly stability and weakly stability of WCT operators are equivalent. Finally we provided some concrete examples to illustrate our main results.