## The spectrum operator of $$\chi^{2}$$ sequence space defined by Musielak Orlicz function.(English)Zbl 1369.40008

Summary: In this paper we have examined various spectra of the operator $$D(p, q, r, s)$$ on the sequence space $$\chi^{2}$$ defined by Musielak Orlicz function.

### MSC:

 40H05 Functional analytic methods in summability 46A35 Summability and bases in topological vector spaces 47A10 Spectrum, resolvent
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### References:

 [1] T.J.I’A. Bromwich, An introduction to the theory of infinite series, Macmillan and Co.Ltd. , 1965, New York. [2] G.H. Hardy, On the convergence of certain multiple series, Proceedings of the Cambridge Philosophical Society, 19 (1917), 86-95. [3] F. Moricz, Extentions of the spaces c and c0 from single to double sequences, Acta Mathematica Hungariga, 57(1-2) (1991), 129-136. · Zbl 0781.46025 [4] F. Moricz and B.E. Rhoades1988. Almost convergence of double sequences and strong regularity of summability matrices, Mathematical Proceedings of the Cambridge Philosophical Society, 104 (1988), 283-294. · Zbl 0675.40004 [5] M. Basarir and O. Solancan, On some double sequence spaces, Journal of Indian Academy Mathematics, 21(2) (1999), 193-200. · Zbl 0978.40002 [6] Avinoy Paul and Binod Chandra Tripathy, Subdivisions of the spectra for the operator D(r; 0; 0; s) over certain sequence spaces, Bol. Soc. Paran. Mat., 3s.Vol. (34 1) (2016), 75-84. · Zbl 1341.40002 [7] A. Turkmenoglu, Matrix transformation between some classes of double sequences, Journal of Institute of Mathematics and Computer Science Maths Series, 12(1) (1999), 23-31. · Zbl 0940.40004 [8] K. Raj and S.K. Sharma 2012. Some new Lacunary strong convergent vector-valued multiplier difference sequence spaces defined by a Musielak-Orlicz function, Acta Mathematica Academiae Nyiregyhaziensis, 28 (2012), 103-120. · Zbl 1289.46008 [9] K. Raj and S.K. Sharma 2013. Ideal convergent sequence spaces defined by a Musielak-Orlicz function, Thai Journal of Mathematics, 11 (2013), 577-587. · Zbl 1297.46009 [10] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel Journal of Mathematics, 10 (1971), 379-390. · Zbl 0227.46042 [11] J. Musielak, Orlicz spaces, Lectures Notes in Math., 1034, Springer-Verlag, 1983. · Zbl 0557.46020 [12] H. Kizmaz, On certain sequence spaces, Canad. Math.Bull., 24 (1981), 169-176. · Zbl 0454.46010 [13] S. Goldberg, Unbounded linear operators, Dover publications Inc. New York, 1985.
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