Fine spectra of upper triangular double-band matrices over the sequence space \(\ell_p\), (\(1 < p < \infty\)). (English) Zbl 1263.47038
From the author’s abstract: The operator \(A(\tilde{r}, \tilde{s})\) on the sequence space \(\ell_p\) is defined by \(A(\tilde{r}, \tilde{s})x = (r_kx_k + s_kx_{k+1})^\infty_{k=0}\), where \(x = (x_k) \in l_p\), and \(\tilde{r}\) and \(\tilde{s}\) are two convergent sequences of nonzero real numbers satisfying certain conditions, \(1 < p < \infty\). The main purpose of this paper is to determine the fine spectrum with respect to Goldberg’s classification of \(A(\tilde{r}, \tilde{s})\). Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of \(A(\tilde{r}, \tilde{s})\).
Reviewer: Ömer Gök (Istanbul)
MSC:
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 47A10 | Spectrum, resolvent |
Keywords:
approximate point spectrum; defect spectrum; compression spectrum; resolvent set; double sequential band matrixCitations:
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