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Strong Boundedness and Strong Convergence in Sequence Spaces

Published online by Cambridge University Press:  20 November 2018

Martin Buntinas  and
Naza Tanović-Miller
Martin Buntinas
Affiliation:
Department of Mathematical Sciences, Loyola University of Chicago, Chicago, Illinois 60626, USA
Naza Tanović-Miller
Affiliation:
Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Yugoslavia
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Abstract

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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.

Keywords

46A4542A1642A24
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 960 - 974
Copyright
Copyright © Canadian Mathematical Society 1991

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