CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE EQUENCES OF ORDER m

doi:10.1016/S0252-9602(11)60332-9

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (4): 1465-1474.doi: 10.1016/S0252-9602(11)60332-9

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CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE EQUENCES OF ORDER m

Ivana Djolovi′c|Eberhard Malkowsky

Technical Faculty, University of Belgrade, VJ 12, 19210 Bor, Serbia； Department of Mathematics, Faculty of Science, Fatih University, 34500 Büyükçekmece, Istanbul, Turkey

Received:2009-05-09 Revised:2010-05-27 Online:2011-07-20 Published:2011-07-20
Supported by:
Research of both authors supported by the research project#144003 of the Serbian Ministry of Science, Technology and Development.

Abstract

Abstract:

In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Baffsar ([17]) defined the Euler spaces of m-th order difference sequences e^r₀( Δ^（m）), e^r_c(Δ^（m） ) and e^r_∞(Δ^（m） ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that pur-pose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c₀, c and l_∞. The main tool for our characterizations is the Hausdorff measure of noncompactness.

Key words: difference sequence spaces of order m, matrix transformations, compact op-erators, Hausdorff measure of noncompactness

CLC Number:

46B15

Ivana Djolovi′c, Eberhard Malkowsky. CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE EQUENCES OF ORDER m[J].Acta mathematica scientia,Series B, 2011, 31(4): 1465-1474.

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CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE EQUENCES OF ORDER m

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