SPECTRA OF THE LOWER TRIANGULAR MATRIX B(r1, . . . , rl ; s1, . . . , sl ′) OVER c0

Abstract

The inĄnite lower triangular matrix B(r1, . . . , rl ; s1, . . . , sl ′ ) is considered over the sequence space c0, where l and l ′ are positive integers. The diagonal and sub-diagonal entries of the matrix consist of the oscillatory sequences r = (rk(mod l)+1) and s = (sk(mod l ′)+1), respectively. The rest of the entries of the matrix are zero. It is shown that the matrix represents a bounded linear operator. Then the spectrum of the matrix is evaluated and partitioned into its Ąne structures: point spectrum, continuous spectrum, residual spectrum, etc. In particular, the spectra of the matrix B(r1, . . . , r4; s1, . . . , s6) are determined. Finally, an example is taken in support of the results