In general, the behaviors of the symmetric tri-band matrices on the Hilbert spaces are well known. But the symmetric tri-band matrices have different behavior on the Banach spaces. The main purpose of this work is to determine the fine spectra of the operator U(s, r, s) defined by symmetric tri-band matrix over the sequence spaces l(p) and bv(p). (C) 2011 Elsevier Ltd. All rights reserved.
