We study the spectrum of multipliers (bounded operators commuting with the shift operator <img border=0 width=15 height=20 id="_x0000_i1052" src="http:/fbpe/img/cubo/v14n3/art02-10.jpg">) on a Banach space <img border=0 width=14 height=24 id="_x0000_i1051" src="http:/fbpe/img/cubo/v14n3/art02-03.jpg"> of sequences on <img border=0 width=17 height=20 id="_x0000_i1050" src="http:/fbpe/img/cubo/v14n3/art02-04.jpg">. Given a multiplier <img border=0 width=20 height=18 id="_x0000_i1049" src="http:/fbpe/img/cubo/v14n3/art02-05.jpg">, we prove that <img border=0 width=129 height=30 id="_x0000_i1048" src="http:/fbpe/img/cubo/v14n3/art02-06.jpg"> where <img border=0 width=23 height=26 id="_x0000_i1047" src="http:/fbpe/img/cubo/v14n3/art02-07.jpg"> is the symbol of <img border=0 width=20 height=18 id="_x0000_i1046" src="http:/fbpe/img/cubo/v14n3/art02-05.jpg">. We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on <img border=0 width=28 height=25 id="_x0000_i1045" src="http:/fbpe/img/cubo/v14n3/art02-08.jpg">. We generalize the results for multipliers on Banach spaces of sequences on <img border=0 width=21 height=23 id="_x0000_i1044" src="http:/fbpe/img/cubo/v14n3/art02-09.jpg">.