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On the Spectrum of Difference Operator Δab Over the Sequence Spaces ℓp and bvp, (1 < p < ¥) |
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PP: 115-120 |
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Author(s) |
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S. Dutta,
P. Baliarsingh,
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Abstract |
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| The main purpose of the present paper is to determine the spectrum of the difference operator Dab over the sequence spaces
ℓp and bvp, (1 < p < ¥). For any two sequences a = (ak) and b = (bk) of distinct, non zero real numbers and satisfying certain
conditions, the difference operator Dab is defined by (Dabx)k = akxk +bk−1xk−1, where (xk) ∈ ℓp or bvp and x−1 = 0. Finally, we
obtain the spectrum, point spectrum, residual spectrum and the continuous spectrum of the difference operator Dab over ℓp and bvp. |
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