Curvature Invariant for Hilbert Modules over Free Semigroup Algebras

By Gelu Popescu. 2001

56 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f38bd55c7ed42aec7f3c77bf4eadd1467fec3e0c

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Citations in the corpus

Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, background): “The curvature invariant has also been defined for row contractions which are not necessarily commutative [85, 99], and this notion has been generalized further for completely positive maps [92].”
Operator theory on noncommutative varieties (2005, background): “Since E is a cyclic subspacefor V1, . . . , Vn, we deduce that k = 0, and therefore AE = L.”
Operator Theory on Noncommutative Domains (2007, unknown): “Introduced in [70] in connection with a multivariable noncommutative von Neumann inequality, the noncommutative analytic Toeplitz algebra F∞ n has been studied in several papers [68], [69], [72], [73], [74], [76], [6], and recently in [35], [36], [37], [8], [78], [39], [64], [81], and [87].”
Unitary Invariants in Multivariable Operator Theory (2004, methodology): “In [52], [5], [6], [3], [2], [17], [53], [ 54 ] and [40], a good case is made that the appropriate multivariable commutative analogue of H ∞ (D) is the algebra W ∞ n := PF”
Free holomorphic functions and interpolation (2007, background): “In the last two decades, significant progress has been made in noncommutative multivariable operator theory regarding noncommutative dilation theory and its applications to interpolation in several variables ([24], [28], [40], [38], [30], [4], [36]), and unitary invariants for n-tuples of operators ”
Free holomorphic automorphisms of the unit ball of B(ℋ) n (2008, methodology): “This enables us to obtain some results concerning the behavior of the curvature and the Euler characteristic of a row contraction (see [26], [13]) under the automorphism group Aut(B(H)1 ).”
Free holomorphic functions on the unit ball of B(H)n (2006, methodology): “We refer to [35,36,44] for more on noncommutative Poisson transforms on C∗-algebras generated by isometries.”
Entropy and Multivariable Interpolation (2003, background): “…noncommutative dilation theory (see [10], [24], [37], [38], [39], [41], [48]), harmonic analysis on Fock spaces (see [39], [40], [41], [44], [51], [2], [14], and [15]), the results of Foia¸s, Frazho, and Gohberg [22] (see also [21], [23], and [66]) on maximal entropy interpolation (case n…”
Similarity and ergodic theory of positive linear maps (2003, methodology): “Using a result from [39], we can prove the following characterization of Hilbert modules isomorphic to finite rank free Hilbert modules.”