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The dual spaces of sets of difference sequences of order m and matrix transformations. (English) Zbl 1123.46007
Summary: Let p=(p k ) k=0 be a bounded sequence of positive reals, m, and u be s sequence of nonzero terms. If x=(x k ) k=0 is any sequence of complex numbers, we write Δ (m) x for the sequence of the m-th order differences of x and Δ u (m) X={x=(x) k=0 :uΔ (m) xX} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δ u (m) X for X=c 0 (p),c(p), (p) and characterize some matrix transformations between these spaces Δ (m) X.
MSC:
46A45Sequence spaces
40H05Functional analytic methods in summability
References:
[1]Lascarides, C. G.: A study of certain sequence spaces of Maddox and a generalization of a theorem of Iyer. Pacific J. Math., 38, 487–500 (1971)
[2]Lascarides, C. G., Maddox, I. J.: Matrix transformations between some classes of sequences. Proc. Camb. Phil. Soc., 68, 99–104 (1970) · doi:10.1017/S0305004100001109
[3]Maddox, I. J.: Continuous and Köthe–Toeplitz duals of certain sequence spaces. Proc. Camb. Phil. Soc., 65, 471–475 (1967)
[4]Simons, S.: The sequence spaces (p ν ) and m(p ν ). Proc. London Math. Soc., 15, 422–436 (1965) · Zbl 0128.33805 · doi:10.1112/plms/s3-15.1.422
[5]Kizmaz, H.: On certain sequence spaces. Canad. Math. Bull., 24, 169–175 (1981) · Zbl 0454.46010 · doi:10.4153/CMB-1981-027-5
[6]Malkowsky, E., Parashar, S. D.: Matrix transformations in spaces of bounded and convergent sequences of order m. Analysis, 17, 87–97 (1997)
[7]Ahmad, Z. U., Mursaleen: Köthe–Toeplitz duals of some new sequence spaces and their matrix maps. Publ.Inst. Math. (Beograd), 42(56), 57–61 (1987)
[8]Malkowsky, E.: Absolute and ordinary Köthe–Toeplitz duals of certain sequence spaces. Publ. Inst. Math. (Beograd), 46(60), 97–104 (1989)
[9]Malkowsky, E., Mursaleen, Q.: Generalized sets of difference sequences, their duals and matrix transformations, Sequence Spaces and Applications, P. K. Jain and E. Malkowsky (Eds.), Narosa, New Delhi, 68–83, 1999
[10]Basarir, M., Et, M.: On some new generalized difference sequence spaces. Period. Math. Hungarica, 35(3), 169–175 (1997) · Zbl 0922.40003 · doi:10.1023/A:1004597132128
[11]Malkowsky, E., Rakočević, V.: An introduction into the theory of sequence spaces and measures of noncompactness. Zbornik Radova, Matematički Institut SANU, Beograd, 9(17), 143–234 (2000)
[12]Hardy, G. H.: Divergent Series, Oxford University Press, Oxford, 1973
[13]Wilansky, A.: Summability through Functional Analysis, North–Holland Mathematical Studies 85, Elsevier Science Publishers, Amsterdam, New York, Oxford, 1984
[14]Malkowsky, E.: A note on the Köthe–Toeplitz duals of generalized sets of bounded and convergent difference sequences. Journal of Analysis, 4, 81–91 (1995)
[15]Grosse-Erdmann, K. G.: Matrix transformations between the sequence spaces of Maddox. J. Math. Anal. Appl., 180(1), 223–238 (1993) · Zbl 0791.47029 · doi:10.1006/jmaa.1993.1398
[16]Malkowsky, E.: Linear operators in certain BK spaces. Bolyai Soc. Math. Stud., 5, 259–273 (1996)