Abstract

The main purpose of the paper is to investigate the spectra of the $q-$Cesàro operator C_q, where $0<q<\infty ,$ on Banach spaces. For $0<q<1,$ the method of the proof is to exhibit a relationship between the operator C_q and a generalized difference operator Δ_ab. Furthermore, for $1<q<\infty ,$ it is shown that the operator C_q is compact on certain Banach spaces. In this case, the spectra of C_q are completely determined.

中文翻译：

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关于 q−Cesàro 算子：有界性、紧凑性和谱

摘要

本文的主要目的是研究光谱 $q-$Cesàro 算子C _q，其中$0<q<\infty ,$在巴拿赫空间上。为了$0<q<1,$证明的方法是展示算子C _q和广义差分算子Δ _ab之间的关系。此外，对于$1<q<\infty ,$结果表明，算子C _q在某些Banach 空间上是紧的。在这种情况下，C _q的光谱完全确定。