On some vector valued multiplier spaces with statistical Cesàro summability

Kama, Ramazan

doi:10.2298/fil1916135k

Cited by 10 publications

(4 citation statements)

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“…There are several results on summability by Nörlund means of Fourier series. The authors [2,4,6,7,9,13,14] have looked into it. This encourages us to research it in both more generalized and particular cases.…”

Section: Resultsmentioning

confidence: 99%

On a New Application of Positive and Decreasing Sequences to Double Fourier Series Associated with (N, p^(1)_m, p^(2)_n)

Sahani¹,

Paudel

Thakur

2022

J. Nep. Math. Soc.

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Section: Resultsmentioning

confidence: 99%

On a New Application of Positive and Decreasing Sequences to Double Fourier Series Associated with (N, p^(1)_m, p^(2)_n)

Sahani¹,

Paudel

Thakur

2022

J. Nep. Math. Soc.

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“…Karakuş gave the vector valued multiplier spaces S Λ (T ) and S wΛ (T ) by means of Λ-convergence and a series of bounded linear operators together with the characterization the completeness of both of the normed spaces S Λ (T ) and S wΛ (T ) via c 0 (X)-multiplier convergence of an operator series, [13]. Quite recently, Karakuş and Başar [15,16] and Kama [9] introduced the vector valued multiplier spaces of almost summability, a generalized almost summability and statistical Cesàro summability, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…In [20], McArthur investigated some closed linear subspaces of the space of the weakly unconditional summable sequences in a Banach space X and gave some inclusion relations between these spaces. One can refer to the Aizpuru et al [1,3], Pérez-Fernández et al [21], Kama and Altay [10], Kama et al [11], Kama [9,12], Karakuş [13], Karakuş and Başar [14,15,16] and Swartz [22,23] for recent studies on multiplier convergent series.…”

Section: Introductionmentioning

confidence: 99%

Riesz multiplier convergent spaces of operator valued series and a version of Orlicz- Pettis theorem

Karakuş¹,

Kama²

2021

Preprint

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It is not usual to characterize an operator valued series via completeness of multiplier spaces. In this study, by using a series of bounded linear operators, we introduce the space M ∞ R k T k of Riesz summability which is a generalization of the Cesàro summability. Therefore, we give the completeness criteria of these spaces with c0(X)-multiplier convergent operator series. It is a natural consequence that one can characterize the completeness of a normed space through M ∞ R k T k which will be assumed that is complete for every c0(X)-multiplier Cauchy operator series. Then, we characterize the continuity and the (weakly) compactness of the summing operator S from the multiplier space M ∞ R k T k to an arbitrary normed space Y through c0(X)-multiplier Cauchy and ℓ∞(X)-multiplier convergent series, respectively. We also prove that if k T k is ℓ∞(X)-multiplier Cauchy, then the multiplier space of weakly Riesz-convergence associated to the operator valued seriesAmong other results, finally, we obtain a new version of the well-known Orlicz-Pettis theorem by using Riesz-summability.

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“…where 1 ≤ p < ∞. Some topological and geometrical properties of Cesàro spaces were studied by Shiue [9] , Leibowitz [10], Jagers [11], Cui and Pluciennik [12], Cui and Hudzik [13], Altay and Kama [14], Kama [15].…”

Section: Preliminaries Background and Notationmentioning

confidence: 99%