Multidimensional weak resolvents and spatial equivalence of normal operators

• Autorzy: Michał Jasiczak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47C05: Operators in algebras
• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 47L99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 173
• Numer: 2
• Strony: 129-147

Daty

wydano

2006

Twórcy

autor

Michał Jasiczak

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/sm173-2-2