Mathematics

CLC number: O177

Property $({\mathit{W}}_{\mathit{E}})$and Property $(\mathit{R})$ for Operator and Its Functions

算子及算子函数的 $(W_E)$性质与 $(R)$性质

¹ School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China
² School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, Shaanxi, China

Received: 18 April 2024

Abstract

By using the topological uniform descent, the necessary and sufficient conditions for which property $(W_E)$ and property $(R)$ hold for bounded linear operators are given. As a consequence of the main result, the stability of property $(W_E)$ and property $(R)$ is studied, and a new judgement for operator functions that satisfy property $(W_E)$ and property $(R)$ is discussed.

摘要

本文运用拓扑一致降标性质，给出了有界线性算子同时满足$(W_E)$性质与$(R)$性质的充要条件。之后利用主要结论，研究了$(W_E)$性质与$(R)$性质的稳定性，并得到了算子函数同时有$(W_E)$性质与$(R)$性质的新判定方法。