Composition Operators on Cesàro Function Spaces

Raj, Kuldip; Pandoh, Suruchi; Jamwal, Seema

doi:10.1155/2014/501057

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“…These operators received considerable attention of several mathematician over the past several decades ( [1], [8], [9], [10], [13], [14], [15] A bounded linear operator A : E Ñ E is called Fredholm if A has closed range, dim(kerA) and co-dim(ranA) are finite.…”

Section: Introductionmentioning

confidence: 99%

Multiplication Operators on Cesàro Sequence Spaces

Komal¹,

Pandoh²,

Raj³

2016

Demonstratio Mathematica

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Abstract. In this paper we characterize the compact, invertible and Fredholm multiplication operators on Cesàro sequence spaces. Introduction and preliminariesLet N be the set of positive integers. The Cesàro sequence space Cespl 2 pNqq is defined asThe space Cespl 2 pNqq is a Banach space under the normCesàro sequence spaces Let u : X Ñ C be a function such that u.f P Cespl 2 pNqq for every f P Cespl 2 pNqq. Then we can define a multiplication transformation M u : Cespl 2 pNqq Ñ Cespl 2 pNqq by M u f " u.f, @ f P Cespl 2 pNqq.

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