# 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)
Some paranormed Riesz sequence spaces of non-absolute type. (English) Zbl 1118.46009
Let $t=\left({t}_{k}\right)$ be a sequence of positive numbers and ${T}_{n}:={t}_{0}+\cdots +{t}_{n}$ $\left(n\in ℕ\right)$. For the weighted mean transformation ${y}_{n}:={T}_{n}^{-1}{\sum }_{k=0}^{n}{t}_{k}{x}_{k},$ the authors introduce the Riesz sequence spaces ${r}_{\infty }^{t}\left(p\right):=\left\{\left({x}_{k}\right)\mid {sup}_{n}|{y}_{n}{|}^{{p}_{n}}<\infty \right\}$, ${r}_{0}^{t}\left(p\right):=\left\{\left({x}_{k}\right)\mid {lim}_{n}|{y}_{n}{|}^{{p}_{n}}=0\right\}$ and ${r}_{c}^{t}\left(p\right):={r}_{0}^{t}\left(p\right)\oplus$ span$\left\{\left(1,1,\cdots \right)\right\}$ (here $p=\left({p}_{n}\right)$ is a bounded sequence with ${p}_{n}>0\right)$ and study some of their properties, such as completeness with respect to a paranorm and characterization of the continuous and the Köthe-Toeplitz duals. It is proved that these spaces are linearly isomorphic to the complete paranormed sequence spaces of Maddox, ${\ell }^{\infty }\left(p\right),$ ${c}_{0}\left(p\right)$ and $c\left(p\right)$, respectively. Some matrix mappings related to the Riesz spaces are characterized.

##### MSC:
 46A45 Sequence spaces 46A35 Summability and bases in topological linear spaces