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November 2006 On the fine spectrum of the generalized difference operator $B(r,s)$ over the sequence space $\ell_1$ and $bv$
Hasan FURKAN, H\"usey\.in B\.ILG\.I\C C, Kuddus\.i KAYADUMAN
Hokkaido Math. J. 35(4): 893-904 (November 2006). DOI: 10.14492/hokmj/1285766434

Abstract

The main purpose of this paper is to determine the fine spectrum of the operator $B(r,s)$ defined by a band matrix over the sequence spaces $\ell_1$ and $bv$. Since the operator $B(r,s)$ is reduced to the right-shift, difference and Zweier matrices in special cases $(r,s)=(0,1),(r,s)=(1,-1) $ and $(r,s)=(r,1-r)$, respectively, our results are more general than the corresponding results in the existing literature.

Citation

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Hasan FURKAN. H\"usey\.in B\.ILG\.I\C C. Kuddus\.i KAYADUMAN. "On the fine spectrum of the generalized difference operator $B(r,s)$ over the sequence space $\ell_1$ and $bv$." Hokkaido Math. J. 35 (4) 893 - 904, November 2006. https://doi.org/10.14492/hokmj/1285766434

Information

Published: November 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1119.47005
MathSciNet: MR2289365
Digital Object Identifier: 10.14492/hokmj/1285766434

Subjects:
Primary: 47B37
Secondary: 47A10

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 4 • November 2006
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