On a binary relation between normal operators

Takateru Okayasu, Jan Stochel, and Yasunori Ueda. "On a binary relation between normal operators." Studia Mathematica 204.3 (2011): 247-264. <http://eudml.org/doc/285818>.

@article{TakateruOkayasu2011,
abstract = {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.},
author = {Takateru Okayasu, Jan Stochel, Yasunori Ueda},
journal = {Studia Mathematica},
keywords = {operator inequality; normal operator; spectral measure; unitary equivalence},
language = {eng},
number = {3},
pages = {247-264},
title = {On a binary relation between normal operators},
url = {http://eudml.org/doc/285818},
volume = {204},
year = {2011},
}

TY - JOUR
AU - Takateru Okayasu
AU - Jan Stochel
AU - Yasunori Ueda
TI - On a binary relation between normal operators
JO - Studia Mathematica
PY - 2011
VL - 204
IS - 3
SP - 247
EP - 264
AB - 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.
LA - eng
KW - operator inequality; normal operator; spectral measure; unitary equivalence
UR - http://eudml.org/doc/285818
ER -