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On the Zweier sequence space

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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.
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Bibliogr. 24 poz.
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