Hokkaido Mathematical Journal

FURKAN Hasan, B\.ILG\.I\C C H\"usey\.in, KAYADUMAN Kuddus\.i,

On the fine spectrum of the generalized difference operator $B(r,s)$ over the sequence space $\ell_1$ and $bv$.

Hokkaido Mathematical Journal, 35 (2006) pp.893-904

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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.

MSC(Primary)47B37
MSC(Secondary)47A10
Uncontrolled KeywordsSpectrum of an operator, generalized difference operator and the sequence spaces $\ell_1$ and $bv$