Double Operator Integrals and Submajorization

D. Potapov; F. Sukochev

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 4, page 317-339
  • ISSN: 0973-5348

Abstract

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We present a user-friendly version of a double operator integration theory which still retains a capacity for many useful applications. Using recent results from the latter theory applied in noncommutative geometry, we derive applications to analogues of the classical Heinz inequality, a simplified proof of a famous inequality of Birman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods are sufficiently strong to treat these inequalities in the setting of symmetric operator norms in general semifinite von Neumann algebras.

How to cite

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Potapov, D., and Sukochev, F.. "Double Operator Integrals and Submajorization." Mathematical Modelling of Natural Phenomena 5.4 (2010): 317-339. <http://eudml.org/doc/197628>.

@article{Potapov2010,
abstract = {We present a user-friendly version of a double operator integration theory which still retains a capacity for many useful applications. Using recent results from the latter theory applied in noncommutative geometry, we derive applications to analogues of the classical Heinz inequality, a simplified proof of a famous inequality of Birman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods are sufficiently strong to treat these inequalities in the setting of symmetric operator norms in general semifinite von Neumann algebras.},
author = {Potapov, D., Sukochev, F.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {double operator integration; unitarily invariant norm inequalities; noncommutative Lp-spaces; noncommutative -spaces},
language = {eng},
month = {5},
number = {4},
pages = {317-339},
publisher = {EDP Sciences},
title = {Double Operator Integrals and Submajorization},
url = {http://eudml.org/doc/197628},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Potapov, D.
AU - Sukochev, F.
TI - Double Operator Integrals and Submajorization
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/5//
PB - EDP Sciences
VL - 5
IS - 4
SP - 317
EP - 339
AB - We present a user-friendly version of a double operator integration theory which still retains a capacity for many useful applications. Using recent results from the latter theory applied in noncommutative geometry, we derive applications to analogues of the classical Heinz inequality, a simplified proof of a famous inequality of Birman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods are sufficiently strong to treat these inequalities in the setting of symmetric operator norms in general semifinite von Neumann algebras.
LA - eng
KW - double operator integration; unitarily invariant norm inequalities; noncommutative Lp-spaces; noncommutative -spaces
UR - http://eudml.org/doc/197628
ER -

References

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