Strong Boundedness and Strong Convergence in Sequence Spaces

Buntinas, Martin ; Tanović-Miller, Naza

Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 960-974

Résumé

Strong convergence has been investigated in summability theory and Fourier analysis. This paper extends strong convergence to a topological property of sequence spaces E. The more general property of strong boundedness is also defined and examined. One of the main results shows that for an FK-space E which contains all finite sequences, strong convergence is equivalent to the invariance property E = l ν0. E with respect to coordinatewise multiplication by sequences in the space lν0 defined in the paper. Similarly, strong boundedness is equivalent to another invariance E = lν.E. The results of the paper are applied to summability fields and spaces of Fourier series.

Détail

DOI : 10.4153/CJM-1991-053-8

Mots-clés : 46A45, 42A16, 42A24

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