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

The inĄnite lower triangular matrix B(r₁, . . ., r_l; s₁, . . ., s_l') 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 = (r_{k(mod l)}+1) and s = (s_{k(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. [ABSTRACT FROM AUTHOR]