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On a binary relation between normal operators

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Okayasu T., Stochel J., Ueda Y.

Studia Mathematica

2011

tom 204

nr 3

247-264

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.

Ograniczanie wyników

1 Studia Mathematica

1 Okayasu T.

1 Stochel J.

1 Ueda Y.

1 2011

Wyniki wyszukiwania

On a binary relation between normal operators