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## Studia Mathematica

2002 | 149 | 1 | 39-62
Tytuł artykułu

### Separate and joint similarity to families of normal operators

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EN
Sets of bounded linear operators 𝓢,𝓣 ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that $G^{-1}·𝓢·G = 𝓣$. A bounded operator is scalar if it is similar to a normal operator. 𝓢 is jointly scalar if there exists a set 𝓝 ⊂ ℬ(H) of normal operators such that 𝓢 and 𝓝 are similar. 𝓢 is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented (Theorems 3.7, 4.4 and 4.6).
Continuous algebra homomorphisms between the algebra of all complex-valued continuous functions on a compact Hausdorff space and the algebra of all bounded operators in a Hilbert space are studied.
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Tom
Numer
Strony
39-62
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Daty
wydano
2002
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autor
• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
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