### Spectra of the Lower Triangular Matrix \$\mathbb{B}(r_1,\ldots,r_l;s_1,\ldots,s_{l'})\$ over \$c_0\$

Authors: S. K. MAHTO, A. PATRA AND P. D. SRIVASTAVA

DOI: 10.46793/KgJMat2203.369M

Abstract:

The inﬁnite lower triangular matrix ????(r1,,rl; s1,,sl) is considered over the sequence space c0, where l and lare 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 ﬁne structures: point spectrum, continuous spectrum, residual spectrum, etc. In particular, the spectra of the matrix ????(r1,,r4; s1,,s6) are determined. Finally, an example is taken in support of the results.

Keywords:

Fine spectra, sequence space, lower triangular inﬁnite matrix, point spectrum, continuous spectrum, residual spectrum.

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