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The Fine Spectra of the Difference Operator Δ Over the Sequence Space bv p , (1 ≤ p < ∞)*

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Abstract

The sequence space bv p consisting of all sequences (x k ) such that (x k − x k−1) belongs to the space ℓ p has recently been introduced by Başar and Altay [Ukrainian Math. J., 55(1)(2003), 136–147]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bv p have been given and the norm of the difference operator Δ acting on the sequence space bv p has been found. The fine spectrum with respect to the Goldberg’s classification of the difference operator Δ over the sequence space bv p has been determined, where 1 ≤ p < ∞.

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Authors and Affiliations

  1. Baku State University, Department of Mech. & Math., Z. Khalilov Str., 23, 370145, Baku, Azerbaijan

    Ali M. Akhmedov

  2. İnönü Üniversitesi, Eğitim Fakültesi, Matematik Eğitimi Bölümü, Malatya, 44280, Türkiye

    F. Başar

Authors
  1. Ali M. Akhmedov
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  2. F. Başar
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Correspondence to Ali M. Akhmedov.

Additional information

The authors wish to express their thanks to TÜBİTAK–BAYG for supplying the financial support by PC-B Programme during the preparation of the present work in winter 2004 and for their common project

This work has been presented in brief in the International Workshop on Analysis and Its Applications, September 07-11, 2004, Mersin, Türkiye

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Akhmedov, A.M., Başar, F. The Fine Spectra of the Difference Operator Δ Over the Sequence Space bv p , (1 ≤ p < ∞)*. Acta Math Sinica 23, 1757–1768 (2007). https://doi.org/10.1007/s10114-005-0777-0

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  • DOI: https://doi.org/10.1007/s10114-005-0777-0

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