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In general, it is well known the behaviors of the symmetric tri-band matriceson the Hilbert spaces. But the symmetric tri-band matrices have different thebehavior on the Banach spaces. The main purpose of this work is to determinethe fine spectra of the operator U(s, r, s) defined by symmetric tri-bandmatrix over the sequence spaces {\ell}_p and bvp.

On the fine spectrum of the second order difference operator over the sequence spaces \ell_p and bv_p, (1 < p < \infty)