Operator representations of function algebras and functional calculus

• Autorzy: Juratoni A. , Suciu N.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

weak*-Dirichlet algebra; Hardy space; operator representation; semispectral measure

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 2
• Strony: 237--255
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Juratoni A.

autor

Suciu N.

• "Politehnica" University of Timişoara Department of Mathematics Piaţa Victoriei No. 2, Et. 2, 300006, Timişoara, Romania,

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