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Zbl 1016.40002
de Malafosse, Bruno
Properties of some sets of sequences and application to the spaces of bounded difference sequences of order $\mu$. (English)
[J] Hokkaido Math. J. 31, No.2, 283-299 (2002). ISSN 0385-4035

The author studies the difference operator $\Delta$ and its powers as operators on the space of sequences $s_r:= \{(x_n)\in \bbfC^\infty\mid\sup_n\{|x_n|/r^n\}< \infty\}$ for some $r> 0$. Obviously these operators can be represented as infinite matrices and in case $r= 1$ the space $s_1$ is just the space of bounded sequences. In this paper, among other things, the spectra of such operators as maps from $s_r$ to $s_r$ are studied and characterizations of infinite matrix mappings from $(\Delta-\lambda I)^{-1}s_r$ to $s_r$ are given.
[Ulrich Stadtmüller (Ulm)]

MSC 2000:: *40C05 Matrix methods in summability
46A45 Sequence spaces
47A10 Spectrum and resolvent of linear operators

Keywords: difference operator; space of sequences; spectra

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