Abstract and Applied Analysis

On the Riesz Almost Convergent Sequences Space

Mehmet Şengönül and Kuddusi Kayaduman

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Abstract

The purpose of this paper is to introduce new spaces f ̂ and f ̂ 0 that consist of all sequences whose Riesz transforms of order one are in the spaces f and f 0 , respectively. We also show that f ̂ and f ̂ 0 are linearly isomorphic to the spaces f and f 0 , respectively. The β - and γ - duals of the spaces f ̂ and f ̂ 0 are computed. Furthermore, the classes ( f ̂ : μ ) and ( μ : f ̂ ) of infinite matrices are characterized for any given sequence space μ and determine the necessary and sufficient conditions on a matrix A to satisfy B R - c o r e ( A x ) K - c o r e ( x ) , B R - c o r e ( A x ) s t - c o r e ( x ) for all x l .

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 691694, 18 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495698

Digital Object Identifier
doi:10.1155/2012/691694

Mathematical Reviews number (MathSciNet)
MR2922916

Zentralblatt MATH identifier
1250.46005

Citation

Şengönül, Mehmet; Kayaduman, Kuddusi. On the Riesz Almost Convergent Sequences Space. Abstr. Appl. Anal. 2012 (2012), Article ID 691694, 18 pages. doi:10.1155/2012/691694. https://projecteuclid.org/euclid.aaa/1355495698


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