Log-majorizations and norm inequalities for exponential operators

Tom 38 / 1997

Fumio Hiai Banach Center Publications 38 (1997), 119-181 DOI: 10.4064/-38-1-119-181


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.


  • Fumio Hiai

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