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On some new difference sequence spaces of non-absolute type. (English) Zbl 1201.40003

Summary: We introduce the spaces \(c_0^{\lambda}(\Delta)\) and \(c^{\lambda}(\Delta)\) of difference sequences which are the \(BK\)-spaces of non-absolute type and prove that these spaces are linearly isomorphic to the spaces \(c_{0}\) and \(c\), respectively. We also derive some inclusion relations. Furthermore, we determine the \(\alpha -, \beta \)- and \(\gamma \)-duals of those spaces and construct their bases. Finally, we characterize some matrix classes concerning the spaces \(c_0^{\lambda}(\Delta)\) and \(c^{\lambda}(\Delta)\).

MSC:

40C05 Matrix methods for summability
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[1] Choudhary, B.; Nanda, S., Functional analysis with applications, (1989), John Wiley & Sons Inc. New Delhi · Zbl 0698.46001
[2] Wang, C.-S., On Nörlund sequence spaces, Tamkang J. math., 9, 269-274, (1978) · Zbl 0415.46009
[3] Ng, P.-N.; Lee, P.-Y., Cesàro sequence spaces of non-absolute type, Comment. math. prace mat., 20, 2, 429-433, (1978) · Zbl 0408.46012
[4] Malkowsky, E.; Savaş, E., Matrix transformations between sequence spaces of generalized weighted means, Appl. math. comput., 147, 2, 333-345, (2004) · Zbl 1036.46001
[5] Malkowsky, E., Recent results in the theory of matrix transformations in sequence spaces, Mat. vesnik, 49, 187-196, (1997) · Zbl 0942.40006
[6] Altay, B.; Başar, F., On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian bull. math., 26, 5, 701-715, (2002) · Zbl 1058.46002
[7] Altay, B.; Başar, F., Some Euler sequence spaces of non-absolute type, Ukrainian math. J., 57, 1, 1-17, (2005) · Zbl 1096.46011
[8] Altay, B.; Başar, F.; Mursaleen, M., On the Euler sequence spaces which include the spaces \(\ell_p\) and \(\ell_\infty\) I, Inform. sci., 176, 10, 1450-1462, (2006) · Zbl 1101.46015
[9] Aydın, C.; Başar, F., On the new sequence spaces which include the spaces \(c_0\) and \(c\), Hokkaido math. J., 33, 2, 383-398, (2004) · Zbl 1085.46002
[10] Aydın, C.; Başar, F., Some new paranormed sequence spaces, Inform. sci., 160, 1-4, 27-40, (2004) · Zbl 1049.46002
[11] Aydın, C.; Başar, F., Some new sequence spaces which include the spaces \(\ell_p\) and \(\ell_\infty\), Demonstratio math., 38, 3, 641-656, (2005) · Zbl 1096.46005
[12] Şengönül, M.; Başar, F., Some new Cesàro sequence spaces of non-absolute type which include the spaces \(c_0\) and \(c\), Soochow J. math., 31, 1, 107-119, (2005) · Zbl 1085.46500
[13] Başarır, M., On some new sequence spaces and related matrix transformations, Indian J. pure appl. math., 26, 10, 1003-1010, (1995) · Zbl 0855.40005
[14] Altay, B.; Başar, F.; Malkowsky, E., Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness, Appl. math. comput., 211, 2, 255-264, (2009) · Zbl 1171.40002
[15] Aydın, C.; Başar, F., Some new difference sequence spaces, Appl. math. comput., 157, 3, 677-693, (2004) · Zbl 1072.46007
[16] Başar, F.; Altay, B., On the space of sequences of \(p\)-bounded variation and related matrix mappings, Ukrainian math. J., 55, 1, 136-147, (2003) · Zbl 1040.46022
[17] Kızmaz, H., On certain sequence spaces, Canad. math. bull., 24, 2, 169-176, (1981) · Zbl 0454.46010
[18] Malkowsky, E.; Mursaleen, M.; Suantai, S., The dual spaces of sets of difference sequences of order \(m\) and matrix transformations, Acta math. sinica, 23, 3, 521-532, (2007) · Zbl 1123.46007
[19] M. Mursaleen, A.K. Noman, On the spaces of \(\lambda\)-convergent and bounded sequences, Thai J. Math. 8 (2) (2010) (in press). · Zbl 1218.46005
[20] Maddox, I.J., Elements of functional analysis, (1988), The University Press Cambridge · Zbl 0193.08601
[21] Wilansky, A., ()
[22] Stieglitz, M.; Tietz, H., Matrixtransformationen von folgenräumen eine ergebnisübersicht, Math. Z., 154, 1-16, (1977) · Zbl 0331.40005
[23] Mursaleen, M.; Başar, F.; Altay, B., On the Euler sequence spaces which include the spaces \(\ell_p\) and \(\ell_\infty\) II, Nonlinear anal. TMA, 65, 3, 707-717, (2006) · Zbl 1108.46019
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