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Abstrakty
This paper deals with some operator representations φ of a weak*-Dirichlet algebra A, which can be extended to the Hardy spaces Hp(m), associated to A and to a representing measure m of A, for 1 ≤ p ≤ ∞. A characterization for the existence of an extension φp of φ to Lp(m) is given in the terms of a semispectral measure Fφ of φ. For the case when the closure in Lp(m) of the kernel in A of m is a simply invariant subspace, it is proved that the map φp/Hp(m) can be reduced to a functional calculus, which is induced by an operator of class Cρ in the Nagy-Foias sense. A description of the Radon-Nikodym derivative of Fφ is obtained, and the log-integrability of this derivative is proved. An application to the scalar case, shows that the homomorphisms of A which are bounded in Lp(m) norm, form the range of an embedding of the open unit disc into a Gleason part of A.
Czasopismo
Rocznik
Tom
Strony
237--255
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
autor
- "Politehnica" University of Timişoara Department of Mathematics Piaţa Victoriei No. 2, Et. 2, 300006, Timişoara, Romania, adinajuratoni@yahoo.com
Bibliografia
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- [11] A. Juratoni, On uniformly stable ρ-contractions, Proc. of PAMM Conference, Balatonalmady (Hungary), BAM-CXIII/2008, Nr. 2382-2398, 017–027.
- [12] A. Juratoni, On operator representations of weak*-Dirichlet algebras, Proc. of the 22nd Conference on Operator Theory, Theta Bucureşti 2010, 89–98.
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- [21] I. Suciu, Function Algebras, Noordhoff Intern. Publ. Leyden, The Netherlands, 1975.
- [22] B.SZ.-Nagy, C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North Holland, New York, 1970.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0005-0005