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## Studia Mathematica

2006 | 173 | 2 | 129-147
Tytuł artykułu

### Multidimensional weak resolvents and spatial equivalence of normal operators

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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.
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Tom
Numer
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129-147
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wydano
2006
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• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
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