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)
Generalized spaces of difference sequences. (English) Zbl 0873.46014
Abstract of the paper: “Let , c and c 0 be the Banach spaces of bounded, convergent and null sequences x=(x k ) 1 , respectively. Write Δx=(x k -x k+1 ) 1 and Δ 2 x=(Δx k -Δx k+1 ) 1 . In [Canad. Math. Bull. 24, 169-176 (1981; Zbl 0454.46010)], H. Kizmaz has introduced and studied the sequence spaces, E(Δ)={x:ΔxE}, where E{c 0 ,c, }. Recently, [Turk. J. Math. 17, No. 1, 18-24 (1993; Zbl 0826.40001)], Mikail Et defined the sets E(Δ 2 )={x:Δ 2 xE}. He obtained α-duals of these sets and characterized the matrix class (E,F(Δ 2 )), where E,F{c 0 ,c, }. In this paper, we generalize these sets and define E(u;Δ 2 )={x:u·Δ 2 xE}, where u=(u k ) is another sequence such that u k 0 (k=1,2,). We obtain α- and β-duals of these sets and further we characterize the matrix classes (E(u;Δ 2 ),F) and (E,F(u;Δ 2 ))”.

46B45Banach sequence spaces
46A45Sequence spaces
40H05Functional analytic methods in summability
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)