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Bişgin, Mustafa Cemil

On the fine spectrum of the operator \(Q (r, s, t, u)\) over \(\ell_p\) and \(bv_p\), \(1 < p < \infty\). (English) Zbl 1507.47077

Rocky Mt. J. Math. 52, No. 3, 777-791 (2022).
Summary: We specify the fine spectrum of the quadruple band matrix operator \(Q (r, s, t, u)\) over the sequence spaces \(\ell_p\) and \(bv_p\), where \(1 < p < \infty\). The quadruple band matrix \(Q (r, s, t, u)\) is the general state of \(\Delta^3\), \(D (r, 0, 0, s)\), \(B (r, s, t)\), \(\Delta^2\), \(B (r, s)\), \(\Delta\), right shift and Zweier matrices, where \(\Delta^3\), \(B (r, s, t)\), \(\Delta^2\), \(B (r, s)\) and \(\Delta\) are called third-order difference, triple band, second-order difference, double band (generalized difference) and difference matrix, respectively.

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B39 Linear difference operators
47A10 Spectrum, resolvent

Keywords:

spectrum of an operator; resolvent set; perturbed operator; quadruple band matrix; sequence spa
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References:

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