Dual algebras generated by von Neumann n-tuples over strictly pseudoconvex sets

Michael Didas. Dual algebras generated by von Neumann n-tuples over strictly pseudoconvex sets. 2004. <http://eudml.org/doc/285934>.

@book{MichaelDidas2004,
abstract = {Let D ⋐ X denote a relatively compact strictly pseudoconvex open subset of a Stein submanifold X ⊂ ℂⁿ and let H be a separable complex Hilbert space. By a von Neumann n-tuple of class over D we mean a commuting n-tuple of operators T ∈ L(H)ⁿ possessing an isometric and weak* continuous $H^\{∞\}(D)$-functional calculus as well as a ∂D-unitary dilation. The aim of this paper is to present an introduction to the structure theory of von Neumann n-tuples of class over D including the necessary function- and measure-theoretical background. Our main result will be a chain of equivalent conditions characterizing those von Neumann n-tuples of class over D which satisfy the factorization property $_\{1,ℵ₀\}$. The dual algebra generated by each such tuple is shown to be super-reflexive. As a consequence we deduce that each subnormal tuple possessing an isometric and weak* continuous $H^\{∞\}(D)$-functional calculus and each subnormal tuple with dominating Taylor spectrum in D is reflexive.},
author = {Michael Didas},
keywords = {-functional calculus; reflexive operators; dual operator algebras; subnormal systems; Henkin measures; inner functions; strictly pseudoconvex sets},
language = {eng},
title = {Dual algebras generated by von Neumann n-tuples over strictly pseudoconvex sets},
url = {http://eudml.org/doc/285934},
year = {2004},
}

TY - BOOK
AU - Michael Didas
TI - Dual algebras generated by von Neumann n-tuples over strictly pseudoconvex sets
PY - 2004
AB - Let D ⋐ X denote a relatively compact strictly pseudoconvex open subset of a Stein submanifold X ⊂ ℂⁿ and let H be a separable complex Hilbert space. By a von Neumann n-tuple of class over D we mean a commuting n-tuple of operators T ∈ L(H)ⁿ possessing an isometric and weak* continuous $H^{∞}(D)$-functional calculus as well as a ∂D-unitary dilation. The aim of this paper is to present an introduction to the structure theory of von Neumann n-tuples of class over D including the necessary function- and measure-theoretical background. Our main result will be a chain of equivalent conditions characterizing those von Neumann n-tuples of class over D which satisfy the factorization property $_{1,ℵ₀}$. The dual algebra generated by each such tuple is shown to be super-reflexive. As a consequence we deduce that each subnormal tuple possessing an isometric and weak* continuous $H^{∞}(D)$-functional calculus and each subnormal tuple with dominating Taylor spectrum in D is reflexive.
LA - eng
KW - -functional calculus; reflexive operators; dual operator algebras; subnormal systems; Henkin measures; inner functions; strictly pseudoconvex sets
UR - http://eudml.org/doc/285934
ER -