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

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

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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References

[1] Cooke R C. Infinite Matrices and Sequence Spaces. London: MacMillan and Co Ltd, 1950

[2] Djolovi′c I, Malkowsky E. A note on compact operators on matrix domains. J Math Anal Appl, 2008,
340(1): 291–303

[3] Djolovi′c I,Malkowsky E.Matrix transformationsand compact operators on some new m-th orderdi?erence
sequences. Appl Math Comput, 2008, 198(2): 700–714

[4] Et M. On some topological properties of generalized di?erence sequence spaces. Int J Math & Math Sci,
2000, 24: 209–220

[5] Gaur A K, Mursaleen M. Di?erence sequence spaces. Int J Math & Math Sci, 1998, 21(11): 701–706

[6] Hardy G H. Divergent Series. London: Oxford University Press, 1973

[7] Jarrah A M, Malkowsky E. Ordinary, absolute and strong summability and marix transformations. Filo-
mat, 2003, 17: 59–78

[8] Khan V A, Mursleen M. Applications of measures of noncompactness in matrix transformations. Appl
Math Lett, 2006, 19(7): 599–606

[9] de Malafosse B. The Banach algebra Sα and applications. Acta Sci Math (Szeged), 2004, 70(1/2): 125–145

[10] de Malafosse B, Malkowsky E. Sets of di?erence sequences of order m. Acta Sci Math (Szeged), 2004,
70(3/4): 659–682

[11] de Malafosse B, Rakoˇcevi′c V. Application of measure of noncompactness in operators on the spaces s_α，s⁰_α ，s^c_α ，l^p_α . J Math Anal Appl, 2006, 323(1): 131–145

[12] Malkowsky E, Parashar S D. Matrix transformations in spaces of bounded and convergent di?erence
sequences of order m. Analysis, 1997, 17: 87–97

[13] Malkowsky E, Rakoˇcevi′c V. The measure of noncompactness of linear operators between spaces of mth-
order di?erence sequences. Studia Sci Math Hungar, 1996, 33: 381–391

[14] Malkowsky E, Rakoˇcevi′c V. An Introduction into the Theory of Sequence Spaces and Measures of Non-
compactness. Zbornik Radova, Matematiˇcki Institut Sanu, Belgrade, 2000, 9(17): 143–234

[15] Malkowsky E, Rakoˇcevi′c V. On matrix domains of triangles. Appl Math Comput, 2007, 189(2): 1146–1163

[16] Polat H, Altay B. On some new Euler di?erence sequence spaces. Southeast Asian Bull Math, 2006, 30(2):
209–220

[17] Polat H, Ba?sar F. Some Euler spaces of di?erence sequences of order m. Acta Math Sci, 2007, 27(2):

254–266

[18] Rakoˇcevi′c V. Measures of noncompactness and some applications. Filomat, 1998, 12 : 87–120

[19] Stieglitz M, Tietz H. Matrixtransformationen von Folgenr¨aumen, eine Ergebnis¨ubersicht, Math Z, 1977,
154: 1–16

[20] Wilansky A. Functional Analysis. New York, Toronto, London: Blaisdell Publishing Co, 1964

[21] Wilansky A. Summability Through Functional Analysis. North-Holland Mathematics Studies 85. Ams-
terdam: North-Holland, 1984

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

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