On the paranormed Nörlund sequence space of nonabsolute type. (English) Zbl 1468.46014

Summary: I. J. Maddox [Q. J. Math., Oxf. II. Ser. 18, 345–355 (1967; Zbl 0156.06602)] defined the space \(\ell(p)\) of the sequences \(x = (x_k)\) such that \(\sum_{k = 0}^{\infty} | x_k |^{p_k} < \infty\). In the present paper, the Nörlund sequence space \(N^t(p)\) of nonabsolute type is introduced and proved that the spaces \(N^t(p)\) and \(\ell(p)\) are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the space \(N^t(p)\) are computed and the basis of the space \(N^t(p)\) is constructed. The classes \((N^t(p) : \mu)\) and \((\mu : N^t(p))\) of infinite matrices are characterized. Finally, some geometric properties of the space \(N^t(p)\) are investigated.


46A45 Sequence spaces (including Köthe sequence spaces)


Zbl 0156.06602
Full Text: DOI


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