Acta mathematica scientia, Series B >
DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r, s) ON SOME MADDOX´S SPACES
Received date: 2012-08-13
Revised date: 2013-04-20
Online published: 2014-03-20
Supported by
The main results of this article was partially presented at First International Conference on Analysis and Applied Mathematics (ICAAM 2012) held October 18-21, 2012 in Gumushane, Turkey at Gumushane University.
The domain of generalized difference matrix B(r, s) in the classical spaces l∞, c, and c0 was recently studied by Kiri¸s¸ci and Ba¸sar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞(B, p), c( B, p), and c0(B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞(B, p), c(B, p), and c0(eB , p) are computed and the bases of the spaces c(B , p) and c0(B, p) are constructed. The final section of this article is devoted to the characterization of the classes (λ(B, p) : μ) and (μ : λ(B, p)), where λ∈ {c, c0, l∞} and μ is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.
Faruk OZGER , Feyzi BASAR . DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B(r, s) ON SOME MADDOX´S SPACES[J]. Acta mathematica scientia, Series B, 2014 , 34(2) : 394 -408 . DOI: 10.1016/S0252-9602(14)60014-X
[1] Ahmad Z U. Mursaleen K¨othe-Toeplitz duals of some new sequence spaces and their matrix maps. Publ Inst Math (Beograd), 1987, 42: 57–61
[2] Akhmedov A M, El-Shabrawy S R. On the fine spectrum of the operator a,b over the sequence space c.Comput Math Appl, 2011, 61(10): 2994–3002
[3] Altay B, Ba¸sar F. On the paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull Math, 2002, 26(5): 701–715
[4] Altay B, Ba¸sar F. Some paranormed sequence spaces of non-absolute type derived by weighted mean. J Math Anal Appl, 2006, 319(2): 494–508
[5] Altay B, Ba¸sar F. Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space. J Math Anal Appl, 2007, 336(1): 632–645
[6] Ayd?n C, Ba¸sar F. Some new paranormed sequence spaces. Inform Sci, 2004, 160: 27–40
[7] Ayd?n C, Altay B. Domain of generalized difference matrix B(r, s) on some Maddox’s spaces. Thai J Math, 2013, 11(1): 87–102
[8] Ba¸sar F. Summability Theory and Its Applications. Bentham Science Publishers, e-books. Monographs, Ístanbul-2012, ISBN: 978-1-60805-420-6
[9] Ba¸sar F, Altay B, Mursaleen M. Some generalizations of the space bvp of p-bounded variation sequences. Nonlinear Anal, 2008, 68(2): 273–287
[10] Ba¸sar F, C¸ akmak A F. Domain of triple band matrix B(r, s, t) on some Maddox´s spaces. Ann Funct Anal, 2012, 3(1): 32–48
[11] Djolovi´c I. On compact operators on some spaces related to matrix B(r, s). Filomat, 2010, 24(2): 41–51
[12] Jarrah A M, Malkowsky E. BK spaces, bases and linear operators. Rendiconti Circ Mat Palermo II, 1990, 52: 177–191
[13] Jarrah A M, Malkowsky E. The space bv(p), its β−dual and matrix transformations. Collect Math, 2004, 55(2): 151–162
[14] Grosse-Erdmann K-G. Matrix transformations between the sequence spaces of Maddox. J Math Anal Appl, 1993, 180: 223–238
[15] K?zmaz H. On certain sequence spaces. Canad Math Bull, 1981, 24(2): 169–176
[16] Kiri¸s¸ci M, Ba¸sar F. Some new sequence spaces derived by the domain of generalized difference matrix. Comput Math Appl, 2010, 60(5): 1299–1309
[17] Lorentz G G. A contribution to the theory of divergent sequences. Acta Math, 1948, 80: 167–190
[18] Maddox I J. Spaces of strongly summable sequences. Quart J Math Oxford, 1967, 18(2): 345–355
[19] Maddox I J. Paranormed sequence spaces generated by infinite matrices. Proc Camb Phil Soc, 1968, 64: 335–340
[20] Maddox I J. Some properties of paranormed sequence spaces. London J Math Soc, 1969, 1(2): 316–322
[21] Malkowsky E. Recent results in the theory of matrix transformations in sequence spaces. Mat Vesnik, 1997, 49: 187–196
[22] Malkowsky E, Mursaleen M. Some matrix transformations between the difference sequence spaces c0(p),c(p) and ?1(p). Filomat, 2001, 15: 353–363
[23] Nanda S. Infinite matrices and almost convergence. J Indian Math Soc, 1976, 40: 173–184
[24] ¨Ozger F, Ba¸sar F. Domain of the double sequential band matrix B(er, es) on some Maddox´s spaces. AIP
Conference Proceedings, 2012, 1470: 152–155
[25] Panigrahi B L, Srivastava P D. Spectrum and fine spectrum of generalized second order difference operator
2uv on sequence space c0. Thai J Math, 2011, 9(1): 57–74
[26] Simons S. The sequence spaces ?(pv) and m(pv). Proc London Math Soc, 1965, 15(3): 422–436
[27] Srivastava P D, Kumar S. Fine spectrum of the generalized difference operator on sequence space ?1.Thai J Math, 2010, 8(2): 7–19
[28] Srivastava P D, Kumar S. Fine spectrum of the generalized difference operator uv on sequence space l1.Appl Math Comput, 2012, 218(11): 6407–6414
/
| 〈 |
|
〉 |