The Spectrum of Second Order Quantum Difference Operator

Abstract

In this study, we give another generalization of second order backward difference operator ∇2 by introducing its quantum analog ∇q2. The operator ∇q2 represents the third band infinite matrix. We construct its domains c0(∇q2) and c(∇q2) in the spaces c0 and c of null and convergent sequences, respectively, and establish that the domains c0(∇q2) and c(∇q2) are Banach spaces linearly isomorphic to c0 and c, respectively, and obtain their Schauder bases and α-, β- and γ-duals. We devote the last section to determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the operator ∇q2 over the Banach space c0 of null sequences.

Topics & Concepts