57 research outputs found

    Schur coupling and related equivalence relations for operators on a Hilbert space

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    For operators on Hilbert spaces of any dimension, we show that equivalence after extension coincides with equivalence after one-sided extension, thus obtaining a proof of their coincidence with Schur coupling. We also provide a concrete description of this equivalence relation in several cases, in particular for compact operators

    Contractively included subspaces of Pick spaces

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    Pick spaces are a class of reproducing kernel Hilbert spaces that generalize the classical Hardy space and the Drury--Arveson reproducing kernel spaces. We give characterizations of certain contractively included subspaces of Pick spaces. These generalize the characterization of closed invariant subspaces of Trent and McCullough, as well as results for the Drury--Arveson space obtained by Ball, Bolotnikov and Fang

    Some automorphism invariance properties for multicontractions

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    In the theory of row contractions on a Hilbert space, as initiated by Popescu, two important objects are the Poisson kernel and the characteristic function. We determine their behaviour with respect to the action of the group of unitarily implemented automorphisms of the algebra generated by creation operators on the Fock space. The case of noncommutative varieties, introduced recently by Popescu, is also discussed

    Algebras of block Toeplitz matrices with commuting entries

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    The maximal algebras of scalar Toeplitz matrices are known to be formed by generalized circulants. The identification of algebras consisting of block Toeplitz matrices is a harder problem, that has received little attention up to now. We consider the case when the block entries of the matrices belong to a commutative algebra A \mathcal{A} . After obtaining some general results, we classify all the maximal algebras for certain particular cases of A \mathcal{A}.Comment: An error in the first version is corrected; main results are unchange

    Matrix valued truncated Toeplitz operators: basic properties

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    Matrix valued truncated Toeplitz operators act on vector-valued model spaces. They represent a generalization of block Toeplitz matrices. A characterization of these operators analogue to the scalar case is obtained, as well as the determination of the symbols that produce the zero operator.Comment: 16 page

    The numerical range of a contraction with finite defect numbers

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    An n-dilation of a contraction T acting on a Hilbert space H is a unitary dilation acting on H \oplus C^n. We show that if both defect numbers of T are equal to n, then the closure of the numerical range of T is the intersection of the closures of the numerical ranges of its n-dilations. We also obtain detailed information about the geometrical properties of the numerical range of T in case n=1

    Nonextreme de Branges-Rovnyak spaces as models for contractions

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    The de Branges--Rovnyak spaces are known to provide an alternate functional model for contractions on a Hilbert space, equivalent to the Sz.-Nagy--Foias model. The scalar de Branges--Rovnyak spaces H(b)\mathcal{H}(b) have essentially different properties, according to whether the defining function bb is or not extreme in the unit ball of H∞H^\infty. For bb extreme the model space is just H(b)\mathcal{H}(b), while for bb nonextreme an additional construction is required. In the present paper we identify the precise class of contractions which have as a model H(b)\mathcal{H}(b) with bb nonextreme.Comment: 15v page

    The characteristic function of a complex symmetric contraction

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    It is shown that a contraction on a Hilbert space is complex symmetric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications are given to the description of complex symmetric contractions with defect indices equal to 2

    Recent results on truncated Toeplitz operators

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    Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and spectra of these operators to properties of their symbols. We also connect these facts with properties of the natural embedding measures associated to these operators

    The invariant subspaces of SβŠ•Sβˆ— S\oplus S^*

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    Using the tools of Sz.-Nagy--Foias theory of contractions, we describe in detail the invariant subspaces of the operator SβŠ•Sβˆ— S\oplus S^* , where S S is the unilateral shift on a Hilbert space. This answers a question of C\^amara and Ross.Comment: 11 pages. Theorem 4.4 correcte
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