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Yuan and Leng (2007) gave a generalization of Ky Fans determinantal inequality, which is a celebrated refinement of the fundamental Brunn-Minkowski inequality $(det (A+B))^{1/n} ge (det A)^{1/n} +(det B)^{1/n}$, where $A$ and $B$ are positive semidefinite matrices. In this note, we first give an extension of Yuan-Lengs result to multiple positive definite matrices, and then we further extend the result to a larger class of matrices whose numerical ranges are contained in a sector. Our result improves a recent result of Liu [Linear Algebra Appl. 508 (2016) 206--213].
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohrs inequality due to Vasic and Kev{c}kic.
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality. An eigenval
Lins theorem states that for all $epsilon > 0$, there is a $delta > 0$ such that for all $n geq 1$ if self-adjoint contractions $A,B in M_n(mathbb{C})$ satisfy $|[A,B]|leq delta$ then there are self-adjoint contractions $A,B in M_n(mathbb{C})$ with $
In the spirit of Grothendiecks famous inequality from the theory of Banach spaces, we study a sequence of inequalities for the noncommutative Schwartz space, a Frechet algebra of smooth operators. These hold in non-optimal form by a simple nuclearity argument. We obtain optim
Henstock and Macbeath asked in 1953 whether the Brunn-Minkowski inequality can be generalized to nonabelian locally compact groups; questions in the same line were also asked by Hrushovski, McCrudden, and Tao. We obtain here such an inequality and pr