Log-majorizations and norm inequalities for exponential operators

Fumio Hiai

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 119-181
  • ISSN: 0137-6934

Abstract

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Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii-Wielandt and the Gelfand-Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden-Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means.

How to cite

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Hiai, Fumio. "Log-majorizations and norm inequalities for exponential operators." Banach Center Publications 38.1 (1997): 119-181. <http://eudml.org/doc/208624>.

@article{Hiai1997,
abstract = {Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii-Wielandt and the Gelfand-Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden-Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means.},
author = {Hiai, Fumio},
journal = {Banach Center Publications},
keywords = {majorization; symmetrically normed ideals; Lidskii-Wielandt and the Gelfand-Naimark theorems; logarithmic majorizations; norm inequalities of Golden-Thompson type; exponential operators; exponential product formula; operator means},
language = {eng},
number = {1},
pages = {119-181},
title = {Log-majorizations and norm inequalities for exponential operators},
url = {http://eudml.org/doc/208624},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Hiai, Fumio
TI - Log-majorizations and norm inequalities for exponential operators
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 119
EP - 181
AB - Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii-Wielandt and the Gelfand-Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden-Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means.
LA - eng
KW - majorization; symmetrically normed ideals; Lidskii-Wielandt and the Gelfand-Naimark theorems; logarithmic majorizations; norm inequalities of Golden-Thompson type; exponential operators; exponential product formula; operator means
UR - http://eudml.org/doc/208624
ER -

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