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The aim of this paper is to answer some questions concerning weak resolvents. Firstly, we investigate the domain of extension of weak resolvents Ω and find a formula linking Ω with the Taylor spectrum. We also show that equality of weak resolvents of operator tuples A and B results in isomorphism of the algebras generated by these operators. Although this isomorphism need not be of the form
(1) X ↦ U*XU,
where U is an isometry, for normal operators it is always possible to find a "large" subspace on which unitary similarity holds. This observation is used to prove that the infinite inflation of the spatial isomorphism between algebras generated by inflations of A and B, respectively, does have the form (1). These facts are generalized to other not necessarily commuting operators. We deal mostly with the self-adjoint case.
(1) X ↦ U*XU,
where U is an isometry, for normal operators it is always possible to find a "large" subspace on which unitary similarity holds. This observation is used to prove that the infinite inflation of the spatial isomorphism between algebras generated by inflations of A and B, respectively, does have the form (1). These facts are generalized to other not necessarily commuting operators. We deal mostly with the self-adjoint case.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
129-147
Opis fizyczny
Daty
wydano
2006
Twórcy
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-2