On a binary relation between normal operators

• Autorzy: Takateru Okayasu , Jan Stochel , Yasunori Ueda
• Języki publikacji: EN

Abstrakty

EN

The main goal of this paper is to clarify the antisymmetric nature of a binary relation ≪ which is defined for normal operators A and B by: A ≪ B if there exists an operator T such that $E_{A}(Δ) ≤ T*E_{B}(Δ)T$ for all Borel subset Δ of the complex plane ℂ, where $E_{A}$ and $E_{B}$ are spectral measures of A and B, respectively (the operators A and B are allowed to act in different complex Hilbert spaces). It is proved that if A ≪ B and B ≪ A, then A and B are unitarily equivalent, which shows that the relation ≪ is a partial order modulo unitary equivalence.

Kategorie tematyczne

• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 47A63: Operator inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 3
• Strony: 247-264

Daty

wydano

2011

Twórcy

autor

Takateru Okayasu

• Yamagata University, Yamagata 990-8560, Japan

autor

Jan Stochel

• Instytut Matematyki, Uniwersytet Jagielloński, Łojasiewicza 6, 30-348 Kraków, Poland

autor

Yasunori Ueda

• Nihon University, Yamagata Senior High School, Yamagata 990-2433, Japan

Identyfikatory

DOI

10.4064/sm204-3-4