Geodesic
Some properties of the matrix class (l suffix alpha,l suffix alpha), 0
Commentationes Mathematicae, Tome 60 (2020) no. 1-2, pp. 23-36.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Throughout the present paper, entries of sequences, infinite series and infinite matrices are real or complex numbers. The class \((\ell_\alpha, \ell_\alpha)\), \(0 \alpha \leq 1\), of all infinite matrices transforming sequences in \(\ell_\alpha\) to sequences in \(\ell_\alpha\) is characterized. The structure of \((\ell_\alpha, \ell_\alpha)\), \(0 \alpha \leq 1\), is then discussed. Following Fridy [\emph{Properties of absolute summability matrices}, Proc. Amer. Math. Soc. 24 (1970), 583--585], a Steinhaus type result involving the class \((\ell_\alpha, \ell_\alpha)\) is also proved.
DOI : 10.14708/cm.v60i1-2.7044
Classification : 40 C 05,40 H 05
Mots-clés : A-transform,Cauchy product, alpha-norm,alpha-normed linear space,Steinhaus type theorem 
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Pinnangudi Narayanasubramanian Natarajan. Some properties of the matrix class (l suffix alpha,l suffix alpha), 0. Commentationes Mathematicae, Tome 60 (2020) no. 1-2, pp.  23-36. doi : 10.14708/cm.v60i1-2.7044. http://geodesic.mathdoc.fr/articles/10.14708/cm.v60i1-2.7044/

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