# zbMATH — the first resource for mathematics

##### Examples
 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.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 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)
Generalization of the sequence space $\ell \left(p\right)$ derived by weighted mean. (English) Zbl 1116.46003
Summary: The sequence space $\ell \left(p\right)$ was introduced and studied by I. J. Maddox [Q. J. Math., Oxf., II. Ser. 18, 345–355 (1967; Zbl 0156.06602)]. In the present paper, the sequence spaces $\ell \left(u,v;p\right)$ of non-absolute type which are derived by the generalized weighted mean are defined and it is proved that the spaces $\ell \left(u,v;p\right)$ and $\ell \left(p\right)$ are linearly isomorphic. Besides this, the $\beta$- and $\gamma$-duals of the space $\ell \left(u,v;p\right)$ are computed and a basis of that space is constructed. Further, it is established that the sequence space ${\ell }_{p}\left(u,v\right)$ has the AD property and the $f$-dual of the space ${\ell }_{p}\left(u,v\right)$ is given. Finally, the matrix mappings from the sequence spaces $\ell \left(u,v;p\right)$ to the sequence space $\mu$ and from the sequence space $\mu$ to the sequence space $\ell \left(u,v;p\right)$ are characterized.

##### MSC:
 46A45 Sequence spaces