Interpolation and Commutant Lifting with Weights
نویسندگان
چکیده
منابع مشابه
Bi-Isometries and Commutant Lifting
In a previous paper, the authors obtained a model for a bi-isometry, that is, a pair of commuting isometries on complex Hilbert space. This representation is based on the canonical model of Sz. Nagy and the third author. One approach to describing the invariant subspaces for such a bi-isometry using this model is to consider isometric intertwining maps from another such model to the given one. ...
متن کاملCommutant Lifting for Commuting Row Contractions
The commutant lifting theorem of Sz.Nagy and Foiaş [22, 21] is a central result in the dilation theory of a single contraction. It states that if T ∈ B(H) is a contraction with isometric dilation V acting on K ⊃ H, and TX = XT , then there is an operator Y with ‖Y ‖ = ‖X‖, V Y = Y V and PHY = XPH. This result is equivalent to Ando’s Theorem that two commuting contractions have a joint (power) d...
متن کاملA Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting
A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to the three chain completion problem. The interpolants are upper triangular operator matrices of which the columns induce contractive operators. The set of all s...
متن کاملRelaxed Commutant Lifting: Existence of a Unique Solution
Abstract. In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting setting, and earlier obtained sufficient conditions turn out not to be necessary conditions. It is also shown that these conditions simplify in certain s...
متن کاملCommutator Lifting Inequalities and Interpolation
In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foiaş, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative commutant lifting theorem. This is used to solve new operator-valued interpolation problems of SchurCarathéodory, Nevanlinna-Pick, and Sarason type on Fock s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2017
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-017-2351-4