Strong Boundedness and Strong Convergence in Sequence Spaces
Copyright policy )Strong Boundedness and Strong Convergence in Sequence Spaces
AbstractStrong 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.
- University of Sarajevo Bosnia and Herzegovina
- Loyola University Chicago United States
strong convergence, Summability and bases in topological vector spaces, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, strong boundedness, \(FK\)-space, Convergence and divergence of infinite limiting processes, Summability and absolute summability of Fourier and trigonometric series, topological property of sequence spaces, summability theory, Sequence spaces (including Köthe sequence spaces), Fourier analysis
strong convergence, Summability and bases in topological vector spaces, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, strong boundedness, \(FK\)-space, Convergence and divergence of infinite limiting processes, Summability and absolute summability of Fourier and trigonometric series, topological property of sequence spaces, summability theory, Sequence spaces (including Köthe sequence spaces), Fourier analysis
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