Operator entropy inequalities
M Moslehian, F Mirzapour, A Morassaei - Colloquium Mathematicum, 2013 - infona.pl
We investigate a notion of relative operator entropy, which develops the theory started by JI
Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A=(A₁ …
Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A=(A₁ …
Some inequalities for spectral geometric mean with applications
S Furuichi, Y Seo - Linear and Multilinear Algebra, 2024 - Taylor & Francis
Recently, the spectral geometric mean has been studied by some papers. In this paper, we
first estimate the Hölder-type inequality of the spectral geometric mean of positive invertible …
first estimate the Hölder-type inequality of the spectral geometric mean of positive invertible …
An extended Lie–Trotter formula and its applications
E Ahn, S Kim, Y Lim - Linear algebra and its applications, 2007 - Elsevier
In this paper we present a class of Lie–Trotter formulae for Hermitian operators including the
formulae derived by Hiai–Petz and Furuta. A Lie–Trotter formula for weighted Log-Euclidean …
formulae derived by Hiai–Petz and Furuta. A Lie–Trotter formula for weighted Log-Euclidean …
Relative operator entropy
JI Fujii, Y Seo - Operator and Norm Inequalities and Related Topics, 2022 - Springer
The relative operator entropy S (A| B) is an operator version of (the minis of) the Kullback-
Leibler divergence in the information theory. It is introduced an extension, called solidarities …
Leibler divergence in the information theory. It is introduced an extension, called solidarities …
[HTML][HTML] Matrix trace inequalities on Tsallis relative entropy of negative order
Y Seo - Journal of Mathematical Analysis and Applications, 2019 - Elsevier
In this paper, we show matrix trace inequalities on the quantum Tsallis relative entropy of
negative order, which includes the quasi geometric mean of positive definite matrices …
negative order, which includes the quasi geometric mean of positive definite matrices …
Reverse inequalities involving two relative operator entropies and two relative entropies
T Furuta - Linear algebra and its applications, 2005 - Elsevier
We shall discuss relation among Tsallis relative operator entropy Tp (A∣ B), the relative
operator entropy S^(A| B) by JI Fujii-Kamei, the Tsallis relative entropy Dp (A∥ B) by …
operator entropy S^(A| B) by JI Fujii-Kamei, the Tsallis relative entropy Dp (A∥ B) by …
Matrix trace inequalities related to the Tsallis relative entropies of real order
M Fujii, Y Seo - Journal of Mathematical Analysis and Applications, 2021 - Elsevier
In this paper, we show matrix trace inequalities related to the Tsallis relative entropy of real
order: For positive definite matrices ρ and σ, and each 0< α≤ 1 D α (ρ| σ)≤− Tr [ρ 1− qq T α …
order: For positive definite matrices ρ and σ, and each 0< α≤ 1 D α (ρ| σ)≤− Tr [ρ 1− qq T α …
Shannon type inequalities for Kapur's entropy
Mathematics | Free Full-Text | Shannon Type Inequalities for Kapur’s Entropy Next Article in
Journal Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from …
Journal Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from …
[HTML][HTML] Some log-majorizations and an extension of a determinantal inequality
An eigenvalue inequality involving a matrix connection and its dual is established, and some
log-majorization type results are obtained. In particular, some eigenvalues inequalities …
log-majorization type results are obtained. In particular, some eigenvalues inequalities …
Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications
T Furuta - Linear algebra and its applications, 2006 - Elsevier
Recently Tsallis relative operator entropy Tp (A∣ B) and Tsallis relative entropy Dp (A∥ B)
are discussed by Furuichi–Yanagi–Kuriyama. We shall show two reverse inequalities …
are discussed by Furuichi–Yanagi–Kuriyama. We shall show two reverse inequalities …