Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+

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=...

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Autor principal:	Petkova,Violeta
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2012
Materias:	Multiplier Toeplitz operator shift operator space of sequences spectrum of multiplier joint spectrum of translations
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300002
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spelling	oai:scielo:S0719-064620120003000022018-10-08Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+Petkova,Violeta Multiplier Toeplitz operator shift operator space of sequences spectrum of multiplier joint spectrum of translations 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">.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.14 n.3 20122012-10-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300002en10.4067/S0719-06462012000300002
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Multiplier Toeplitz operator shift operator space of sequences spectrum of multiplier joint spectrum of translations
spellingShingle	Multiplier Toeplitz operator shift operator space of sequences spectrum of multiplier joint spectrum of translations Petkova,Violeta Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
description	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">.
author	Petkova,Violeta
author_facet	Petkova,Violeta
author_sort	Petkova,Violeta
title	Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
title_short	Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
title_full	Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
title_fullStr	Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
title_full_unstemmed	Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+
title_sort	spectral results for operators commuting with translations on banach spaces of sequences on zk and z+
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2012
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300002
work_keys_str_mv	AT petkovavioleta spectralresultsforoperatorscommutingwithtranslationsonbanachspacesofsequencesonzkandz
_version_	1714206778970865664

Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+

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