# On a binary relation between normal operators

Takateru Okayasu; Jan Stochel; Yasunori Ueda

Studia Mathematica (2011)

- Volume: 204, Issue: 3, page 247-264
- ISSN: 0039-3223

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topTakateru 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 -

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