Naslov
Improved variants of Young, Heinz and Hölder inequalities for matrices

Autori
Mario Krnić

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
3rd International Conference on Applied Mathematics and Approximation Theory, TOBB University of Economics and Technology

Mjesto i datum
Ankara, Turska, 28.05.2015. - 31.05.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Young inequality; Heinz inequality; H\"{;o};lder inequality; Hilbert-Schmidt norm; Unitarily invariant norm; Positive semidefinite matrix

Sažetak
In this talk we deal with a more precise estimates for the matrix versions of Young, Heinz, and H\"{;o};lder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert-Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert-Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Finally, we give the refinement and the reverse of the matrix H\"{;o};lder inequality which holds for every unitarily invariant norm. As applications, we also obtain improvements of some well-known matrix inequalities in a quotient form. Our results are compared with the previously known from the literature.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA