On Geometric Series of Positive Linear Operators

Păltănea, Radu

doi:10.33205/cma.506015

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Theorem 12 ([3 Theorem 9]1

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2020

2024

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Cited by 3 publications

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“…The problem of finding the norm of matrix operators on the sequence space p have been studied extensively by many mathematicians and abundant literature exists on the topic. Although topological properties and inclusion relations of b r,s (p) have largely been explored [4,13,12], computing the norm of binomial operators on sequence spaces has not been investigated to date. More recently, the author has computed the norm of operators on several sequence spaces, [7,8,21,22,14,15,16,17,18,20,19].…”

Section: Theorem 12 ([3 Theorem 9]mentioning

confidence: 99%

Binomial Operator as a Hausdorff Operator of the Euler Type

Roopaei

2020

Constructive Mathematical Analysis

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In this paper, we prove that the binomial operator is a Hausdorff operator of the Euler type and consequently, the binomial matrix domain associated with this operator is nothing new except an Euler sequence space. Therefore, all the results of published papers on the binomial sequence spaces like [4], can be extracted easily from [1] and the relation between the binomial and Euler operators that we introduce. Moreover, we compute the norm and the lower bound of the binomial operator on some sequence spaces.

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