EQUIVALENCE ON HIROSHIMA'S TYPE INEQUALITIES FOR POSITIVE SEMIDEFINITE BLOCK MATRICES.

In this paper, we prove that some Hiroshima's type inequalities for positive semidefinite block matrices are equivalent. These interesting results are due to Hiroshima [Phys. Rev. Lett. 91, (2003), 057902], Lin and Wolkowicz [Linear Multilinear Algebra 60, 11-12 (2012), 1365-1368], Turkmen, Paksoy and Zhang [Linear Algebra Appl. 437, 6 (2012), 1305-1316], Zhang and Xu [J. Math. Inequal. 14, 4 (2020), 1383-1388], respectively. [ABSTRACT FROM AUTHOR]