2024 AIOT Best Paper Award Webinar by Prof. Hiroaki Tohyama

Advances in Operator Theory (AIOT) presents best paper award yearly . The award in the year n is given to the best paper published in the years n-1 and n-2. Professor Hiroaki Tohyama was selected to present the 2024 webinar on April 26, 2024.
Published in Mathematics
Like

Share this post

Choose a social network to share with, or copy the URL to share elsewhere

This is a representation of how your post may appear on social media. The actual post will vary between social networks

Professor Hiroaki Tohyama

Professor, Department of Informatics, Maebashi Institute of Technology
Bio: Hiroaki Tohyama received Ph.D. degree in Applied Information and System Engineering from Tokyo Denki University in 1997. During 1997–1998, he stayed in Tokyo Denki University and from 1998 in Maebashi Institute of Technology. He interests in the computational complexity theory of the theoretical computer science. His recent work is "Complexity of the Police Officer Patrol Problem", Journal of Information Processing, Vol. 30, pp. 307-314 (2022) available from https://doi.org/10.2197/ipsjjip.30.307. In 2008, he had started a study group on the relative operator entropies and related topics with Kamei, Watanabe and et. al.
Abstract
The relative operator entropy is defined as S(AB)=A12(logA12BA12)A12  and the Tsallis relative operator entropy as Tx(AB)=A x BAx  for strictly positive operators A and B on a Hilbert space. We extend these relative operator entropies to the n-th relative operator entropies S[n](AB) and Tx[n](AB) based on the Taylor expansion. Furthermore, we generalize those entropies to the n-th residual relative operator entropy Rx,y[n](AB). By using them, we introduce operator valued divergences which are extensions of the α-divergence. We construct new inequalities among those relative operator entropies and operator valued divergences. Those inequalities contain a refinement of Young's inequality as a special case.
References
1. H. Tohyama et al. (2023) Operator valued inequalities based on Young’s inequality. Advances in Operator Theory
2. H. Isa et al. (2020) The n-th relative operator entropies and the n-th operator divergences. Annals of Functional Analysis
3.H. Tohyama et al. (2020) The n-th residual relative operator entropy $${\mathfrak {R}}^{[n]}_{x,y}(A|B)$$. Advances in Operator Theory
4. H. Tohyama et al. (2022) Operator inequalities related to Young’s inequality. Advances in Operator Theory
Grants
Japan Society for the Promotion of ScienceJP23K03132.

Hiroaki Tohyama received Ph.D. degree in Applied Information and System Engineering from Tokyo Denki University in 1997. During 1997–1998, he stayed in Tokyo Denki University and from 1998 in Maebashi Institute of Technology. He interests in the computational complexity theory of the theoretical computer science. His recent work is "Complexity of the Police Officer Patrol Problem", Journal of Information Processing, Vol. 30, pp. 307-314 (2022) available from https://doi.org/10.2197/ipsjjip.30.307 . In 2008, he had started a study group on the relative operator entropies and related topics with Kamei, Watanabe and et. al.

Please sign in or register for FREE

If you are a registered user on Research Communities by Springer Nature, please sign in

Follow the Topic

Operator Theory
Mathematics and Computing > Mathematics > Analysis > Operator Theory