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Zbl 1193.47006
Karakaya, Vatan; Altun, Muhammed
Fine spectra of upper triangular double-band matrices.
(English)
[J] J. Comput. Appl. Math. 234, No. 5, 1387-1394 (2010). ISSN 0377-0427

Let $c_0$ be the space of all null sequences. Let $c$ be the space of all convergent sequences. Let $$V= \pmatrix r & s & 0 & 0 &\cdots\\ 0 & r & s & 0 &\cdots\\ 0 & 0 & r & s &\cdots\\ \cdots &&\cdots&&\ddots\\ \cdots &&\cdots &&\ddots\endpmatrix$$ be an upper triangular double-band infinite matrix. The operator on $c_0$ corresponding to the matrix $V$ is denoted by $(V,c_0)$. Then the point spectrum is $\sigma_p(V,c_0)= \{\lambda\in\bbfC:|\lambda- r|<|s|\}$, the residual spectrum $\sigma_r(V,c_0)= \emptyset$, the continuous spectrum $\sigma_c(V,c_0)= \{\lambda\in \bbfC:|\lambda-r|= |s|\}$. Similarly, $\sigma_p(V,c)$, $\sigma_r(V,c)$ and $\sigma_c(V,c)$ are evaluated. Some applications of these results are given.
[K. Chandrasekhara Rao (Kumbakonam)]
MSC 2000:
*47A10 Spectrum and resolvent of linear operators
47B37 Operators on sequence spaces, etc.

Keywords: spectrum of an operator; infinite matrices; sequence spaces

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