zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Properties of some sets of sequences and application to the spaces of bounded difference sequences of order $\mu$. (English) Zbl 1016.40002
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.

40C05Matrix methods in summability
46A45Sequence spaces
47A10Spectrum and resolvent of linear operators