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1
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Log-majorizations and norm inequalities for exponential operators

100%
Hiai F.
Banach Center Publications
|
1997
|
tom 38
|
nr 1
119-181
EN
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.
2
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A new approach to mutual information

63%
Hiai F., Petz D.
Banach Center Publications
|
2007
|
tom 78
|
nr 1
151-164
EN
A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
3
Content available remote

A free analogue of the transportation cost inequality on the circle

63%
Hiai F., Petz D.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
199-206
4
Content available remote

A new approach to mutual information. II

63%
Hiai F., Miyamoto T.
Banach Center Publications
|
2010
|
tom 89
|
nr 1
143-163
EN
A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.
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