Warianty tytułu
Abstrakty
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 𝔸 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 𝔸 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 𝔸 over D which satisfy the factorization property $𝔸_{1,ℵ₀}$. 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.
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
425
Liczba stron
77
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2004
Twórcy
autor
- Fachrichtung 6.1 - Mathematik, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saarbrücken, Germany
Bibliografia
Języki publikacji
EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm425-0-1
Identyfikatory
DOI
10.4064/dm425-0-1
Kolekcja
DML-PL
