arXiv subjects
Publications and source records attributed to Venus Kaleibary.
In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Aczél inequality and its reverse via generalized Kantorovich constant.
In this paper we present some reverses of the Golden-Thompson type inequalities: Let $H$ and $K$ be Hermitian matrices such that $ e^s e^H \preceq_{ols} e^K \preceq_{ols} e^t e^H$ for some scalars $s \leq t$, and $α\in [0 , 1]$. Then for all $p>0$ and $k =1,2,\ldots, n$ \begin{align*} \label{} λ_k (e^{(1-α)H + αK} ) \leq (\max \lbrace S(e^{sp}), S(e^{tp})\rbrace)^{\frac{1}{p}} λ_k (e^{pH} \sharp_αe^{pK})^{\frac{1}{p}}, \end{align*} where $A\sharp_αB = A^\frac{1}{2} \big ( A^{-\frac{1}{2}} B^\frac{1}{2} A^{-\frac{1}{2}} \big) ^αA^\frac{1}{2}$ is $α$-geometric mean, $S(t)$ is the so called Specht's ratio and $\preceq_{ols}$ is the so called Olson order. The same inequalities are also provided with other constants. The obtained inequalities improve some known results.
In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Aczél inequality dealing with the weighted geometric mean.