Separate and joint similarity to families of normal operators

• Autorzy: Piotr Niemiec
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 1
• Strony: 39-62

Daty

wydano

2002

Twórcy

autor

Piotr Niemiec

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/sm149-1-3