dc.creator | Bermudo Navarrete, Sergio | es |
dc.creator | Hernández Mancera, Carmen | es |
dc.creator | Paúl Escolano, Pedro José | es |
dc.date.accessioned | 2021-09-13T13:21:36Z | |
dc.date.available | 2021-09-13T13:21:36Z | |
dc.date.issued | 1995 | |
dc.identifier.citation | Bermudo Navarrete, S., Hernández Mancera, C. y Paúl Escolano, P.J. (1995). Lifting the solutions of a Toeplitz type equation; the semigroup case X = TsXT*s. Note di Matematica, 1 (2005/2006), 231-257. | |
dc.identifier.issn | 1123-2536 | es |
dc.identifier.uri | https://hdl.handle.net/11441/125649 | |
dc.description.abstract | A Toeplitz operator with respect to a contractive representation {Ts} of an
abelian semigroup Σ in a Hilbert space H is an operator X ∈ B(H) such that X = TsXT
∗
s
for all s ∈ Σ. We show that if {Ts} has a minimal isometric dilation {Us} ⊂ B(K), then
Toeplitz operators can be obtained in a unique way as compressions of operators Y ∈ B(K),
called Toeplitz symbols, such that Y = UsY U
∗
s . This approach to lifting the Toeplitz equation
X = TsXT
∗
s is shown to be unitarily equivalent to the one proposed by Muhly in 1972. We use
our approach to extend to this case a number of theorems about classical Toeplitz operators
and, finally, we show that some classes of well-known operators —like Wiener-Hopf operators,
Toeplitz operators in H2
(T
d
) or Toeplitz operators in the sense of Murphy— fall within the
class studied in this paper. The main objective of this paper is to provide a general framework
that, we hope, will be useful in order to extend to wider classes of operators some of the more
recent and deep advances in the theory of Toeplitz operators. | es |
dc.description.sponsorship | Ministerio de Ciencia y Tecnología BFM2001-3735 | es |
dc.format | application/pdf | es |
dc.format.extent | 27 p. | es |
dc.language.iso | eng | es |
dc.publisher | Universita del Salento | es |
dc.relation.ispartof | Note di Matematica, 1 (2005/2006), 231-257. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Toeplitz operators | es |
dc.subject | Wiener-Hopf operators | es |
dc.subject | Operator semigroups | es |
dc.subject | Minimal isometric dilation | es |
dc.title | Lifting the solutions of a Toeplitz type equation; the semigroup case X = TsXT*s | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) | es |
dc.relation.projectID | BFM2001-3735 | es |
dc.relation.publisherversion | http://siba-ese.unisalento.it/index.php/notemat/article/view/1055 | es |
dc.identifier.doi | 10.1285/i15900932v25n1p231 | es |
dc.journaltitle | Note di Matematica | es |
dc.publication.volumen | 1 | es |
dc.publication.issue | 2005/2006 | es |
dc.publication.initialPage | 231 | es |
dc.publication.endPage | 257 | es |
dc.identifier.sisius | 6624496 | es |