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Zbl 0989.47023
Yildirim, M.
On the spectrum of the Rhaly operators on $\ell_p$. (English)
[J] Indian J. Pure Appl. Math. 32, No.2, 191-198 (2001). ISSN 0019-5588; ISSN 0975-7465/e

Summary: In Bull. Lond. Math. Soc. 21, No. 4, 399-406 (1989; Zbl 0695.47024), {\it H. C. Rhaly} jun. determined the spectrum $R_a$, the Rhaly operator which is represented by the matrix $$R_a= \pmatrix a_0 & 0 & 0 &\cdots\\ a_1 & a_1 & 0 &\cdots\\ a_2 & a_2 & a_2 &\cdots\\ \cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot\\ \cdot &\cdot &\cdot &\cdot\endpmatrix$$ regarded as an operator on the Hilbert space $\ell_2$ normed by $\|x\|= (\sum_n|x_n|^2)^{1/2}$. It is the purpose of this paper to determine the spectrum of Rhaly operator $R_a$ as an operator on the spaces $\ell_p$ of all sequence $x$ such that $\sum_n|x_n|^p< \infty$ holds.

MSC 2000:: *47B37 Operators on sequence spaces, etc.

Keywords: Cesàro operator; point spectrum; Rhaly operator

Citations: Zbl 0695.47024

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