Fine Spectra of Upper Triangular Double-Band Matrices over the Sequence Space ℓp, (1

Abstract EN

The operator A(r̃,s̃) on sequence space on ℓp is defined A(r̃,s̃)x=(rkxk+skxk+1)k=0∞, where x=(xk)∈ℓp, and r̃ and s̃ are two convergent sequences of nonzero real numbers satisfying certain conditions, where (1

The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the operator A(r̃,s̃) defined by a double sequential band matrix over the sequence space ℓp.

Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator A(r̃,s̃) over the space ℓp.