Montes Rodríguez, Alfonso2017-06-212017-06-212005Bermudo Navarrete, S., Marcantognini, S.A.M. y Morán, M.D. (2005). A parametrization for the symbols of a Hankel type operator. En First Advanced Course in Operator Theory and Complex Analysis (71-77), Sevilla: Editorial Universidad de Sevilla.9788447210244http://hdl.handle.net/11441/61420Hankel operators and their symbols, as generalized by V. Pták and P. Vrbová, are considered. In this more general framework, a linear operator X from a Hilbert space H1 to a Hilbert space H2 is said to be a Hankel operator for given contractions T1 on H1 and T2 on H2 if, and only if, XT ∗ 1 = T2X and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations V1 of T1 and V2 of T2. A Hankel symbol of X is a dilation Z of X, with a certain norm constraint, such that ZV ∗ 1 = V2Z. The boundedness condition imposed to X has revealed to be essential, indeed necessary and sufficient, for X to admit Hankel symbols. As for a description of the symbols of X, this work provides a parametric labeling of all of them by means of Schur like formula. As a by-product, a new proof of the existence of Hankel symbols is obtained. The proof is established by associating to X, T1 and T2 a suitable isometry V so that there is a bijective correspondence between the symbols of X and the family of all minimal unitary extensions of V.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess