Commutant lifting for commuting row contractions
نویسندگان
چکیده
منابع مشابه
Commutant 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 کاملThe functional calculus for commuting row contractions
A commuting row contraction is a d-tuple of commuting operators T1, . . . , Td such that ∑d i=1 TiT ∗ i ≤ I. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers Ad on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-∗ continuous functional calculus on the full multiplier algebra. In ...
متن کاملCommutant lifting theorem for n-tuples of contractions
We show that the commutant lifting theorem for n-tuples of commuting contractions with regular dilations fails to be true. A positive answer is given for operators which ”double intertwine” given n-tuples of contractions. The commutant lifting theorem is one of the most important results of the Sz. Nagy—Foias dilation theory. It is usually stated in the following way: Theorem. Let T and T ′ be ...
متن کاملBi-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 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 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: Bulletin of the London Mathematical Society
سال: 2010
ISSN: 0024-6093
DOI: 10.1112/blms/bdq016