The curvature invariant of a non-commutingn-tuple
TLDR
In this paper, non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commuting n-tuple of operators are introduced, which can be thought of as measuring the freeness or curvature of an ann-tree.Abstract:
Non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commutingn-tuple of operators are introduced. The non-commutative curvature invariant is sensitive enough to determine if ann-tuple is free. In general both invariants can be thought of as measuring the freeness or curvature of ann-tuple. The connection with dilation theory provides motivation and exhibits relationships between the invariants. A new class of examples is used to illustrate the differences encountered in the non-commutative setting and obtain information on the ranges of the invariants. The curvature invariant is also shown to be upper semi-continuous.read more
Citations
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Free holomorphic functions on the unit ball of B(H)n
TL;DR: In this article, a non-commutative version of Julia's lemma for free holomorphic functions with operator-valued coefficients was proposed. But this lemma does not guarantee the radial infimum property.
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Operator theory on noncommutative varieties
TL;DR: In this paper, a dilation theory on noncommutative varieties determined by row contractions T: = [T 1,..., T n ] subject to constraints such as p(T 1,...,T n ) = 0, p ∈ P, where T is a set of non commutative polynomials.
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Operator Theory on Noncommutative Domains
TL;DR: In this article, the authors studied non-commutative domains with positive regular free holomorphic functions on a Hilbert space, where the algebra of all bounded linear operators on the Hilbert space was studied.
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Unitary invariants in multivariable operator theory
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Subalgebras of C*-algebras III: multivariable operator theory
TL;DR: In this paper, it was shown that many of the operator-theoretic aspects of function theory in the unit disk generalize to the unit ball B_d in complex d-space, including von Neumann's inequality and the model theory of contractions.
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Isometric dilations for infinite sequences of noncommuting operators
TL;DR: In this article, a dilation theory for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for { Tn }I are obtained.
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Invariant Subspaces and Hyper-Reflexivity for Free Semigroup Algebras
TL;DR: In this paper, the invariant subspace structure of a class of semigroup algebras, called hyper-reflexive, is described algebraically by S∗ i Sj = δijI for 1 ≤ i, j ≤ n; (F)