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Infinite matrices and sigma(A)-core

100%

Kayaduman K. , Furkan H.

2006

tom Vol. 39, nr 3

531-538

In [8], the concepts of sigma-core of a bounded number sequence x have been introduced and also some inequalities which are analogues of Knopp's core theorem have been proved. In this paper, using the concept of Vsigma(A)-summabiIity introduced by Savas, we characterize the matrices of the class (Vmu, Vsigma(A))reg and determine necessary and sufficient conditions for a matrix B to satisfy qsigma(A) (Bx) C qmu(x) for all x is an element of m.

On the Zweier sequence space

80%

Sengonul M.

2007

tom Vol. 40, nr 1

181-196

The purpose of this paper is to introduce the Zweier sequence spaces Ż and Ż0 consisting of all sequences x = (xk) such that (Zx) in the space c and c0 respectively, which is normed. Also, prove that Ż and Ż0 are linearly isomorphic to the space c and c0 respectively. Additionally, the alpha, beta and gamma -duals of the spaces Ż and Ż0 have been computed and space of Ż0 Schauder base have been constructed. Furthermore, given the two theorem concerning matrix map. Finally, the norm of Zweier operator have been given and the .ne spectrum of the Zweier operator over the sequence spaces c and c0 has been determined.