On q−Cesàro Operators: Boundedness, Compactness and Spectra

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.

Keywords:

• Cesàro operators
• sequence spaces
• spectrum

2010 MATHEMATICS SUBJECT CLASSIFICATION::

• Primary 47A10
• Secondary 47B37
• 46B45