The Riesz Core of a Sequence

Yıl 2011, Cilt: 24 Sayı: 1, 35 - 39, 14.01.2011

Celal Çakan Abdullah Alotaıbı

Öz

 The Riesz sequence space q

cr including the space c has recently been defined in [14] and its some properties
have been investigated. In the present paper, we introduce a new type core, Kq-core, of a complex valued
sequence and also determine the required conditions for a matrix B for which Kq-core (Bx) ⊆ K-core (x), Kqcore (Bx) ⊆ stA-core (x) and Kq-core (Bx) ⊆ Kq-core (x) hold for all x ∈ ∞ A . 

Anahtar Kelimeler

Matrix transformations, core of a sequence, statistical convergence

Kaynakça

• Abdullah M. Alotaibi, “Cesáro statistical core of complex number sequences”, Inter. J. Math. Math. Sci., Article ID 29869 (2007).
• B. Altay, F. Başar, “Some paranormed Riesz sequence spaces of non-absolute type”, Southeast Asian Bull. Math. 30(5): 591-608 (2006).
• F. Başar, “A note on the triangle limitation methods”, Fırat Univ. Fen & Müh. Bil. Dergisi, 5(1): 113-117 (1993).
• R. G. Cooke, “Infinite matrices and sequence spaces”, Macmillan, New York (1950).
• J. Connor, “On strong matrix summability with respect to a modulus and statistical convergence”, Canad. Math. Bull. 32: 194-198 (1989).
• C. Çakan, H. Çoşkun, “Some new inequalities related to the invariant means and uniformly bounded function sequences”, Applied Math. Lett. 20(6): 605-609 (2007).
• H. Çoşkun, C. Çakan, “A class of statistical and σ- conservative matrices”, Czechoslovak Math. J. 55(3): 791-801 (2005).
• H. Çoşkun, C. Çakan, Mursaleen, “On the statistical and σ –cores”, Studia Math. 154(1):(2003).
• K. Demirci, “A-statistical core of a sequence”, Demonstratio Math., 33: 43-51 (2000).
• H. Fast, “Sur la convergence statisque”, Colloq. Math., 2: 241-244 (1951).
• A. R. Freedman, J. J. Sember, “Densities and summability”, Pasific J. Math., 95:293-305 (1981).
• J. A. Fridy, C. Orhan, “Statistical core theorems”, J. Math. Anal. Appl., 208: 520-527 (1997).
• I. J. Maddox, “Elements of Functional Analysis”, Cambridge University Press, Cambridge (1970).
• E. Malkowsky, V. Rakoćević, “Measure of noncompactness of linear operators between spaces of sequences that are (N, q) summable or bounded”, Czechoslovac Math. J., 51(126): 505- 522 (2001).
• G. M. Petersen, “Regular matrix transformations”, McGraw-Hill, (1966).
• A. A. Shcherbakov, “Kernels of sequences of complex numbers and their regular transformations”, Math. Notes, 22: 948-953 (1977).