Fuglede-type decompositions of representations

Marek Kosiek

Studia Mathematica (2002)

  • Volume: 151, Issue: 1, page 87-98
  • ISSN: 0039-3223

Abstract

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It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.

How to cite

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Marek Kosiek. "Fuglede-type decompositions of representations." Studia Mathematica 151.1 (2002): 87-98. <http://eudml.org/doc/284507>.

@article{MarekKosiek2002,
abstract = {It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.},
author = {Marek Kosiek},
journal = {Studia Mathematica},
keywords = {band of measures; representation; commutant; contractions; hyperinvariant subspaces; Lebesgue-type decomposition; von Neumann-type inequality},
language = {eng},
number = {1},
pages = {87-98},
title = {Fuglede-type decompositions of representations},
url = {http://eudml.org/doc/284507},
volume = {151},
year = {2002},
}

TY - JOUR
AU - Marek Kosiek
TI - Fuglede-type decompositions of representations
JO - Studia Mathematica
PY - 2002
VL - 151
IS - 1
SP - 87
EP - 98
AB - It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.
LA - eng
KW - band of measures; representation; commutant; contractions; hyperinvariant subspaces; Lebesgue-type decomposition; von Neumann-type inequality
UR - http://eudml.org/doc/284507
ER -

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