arXiv subjects
Publications and source records attributed to A. Sheikhhosseini.
In this paper, by implementing the generalized inverse, known as the Moore-Penrose inverse, for Hilbert space operators, several inner product bounds that are of Cauchy-Schwarz type are presented. As a standard application, some new refined and generalized versions of numerical radius-norm bounds are also stated, in a generalized form that involves different combinations of operators.
In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are investigated. Among other results, it is shown that if $A, B, C, D$ are $n\times n$ positive definite matrices, then \begin{equation*} \left(αA+βB\right)^r\circ\left(αC+βD\right)^{1-r}\leq α\left(A^r\circ C^{1-r}\right)+β\left(B^r\circ D^{1-r}\right), \end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for the Hadamard product.
In this note, some inequalities involving operator means of sectorial matrices are proved which are generalizations and refinements of previous known results. Among them, let $A$ and $B$ be two accretive matrices with $A,B\in\mathcal{S}_θ$, $0 < mI \leqslant A, B \leqslant MI$ for positive real numbers $ M, m, \, σ$ be an operator mean and $σ^{*}$ be the adjoint mean of $ σ.$ If $σ^*\leqslant σ_1,σ_2\leqslant σ$ and $Φ$ is a positive unital linear map, then $$Φ^{p}\Re(A σ_{1} B) \leqslant \sec^{2p}θα^{p} Φ^{p}\Re(A σ_{2} B),$$ where $$ α= \max \left \lbrace K, 4^{1-\frac{2}{p}}K \right \rbrace,$$ and $ K= \frac{(M+m)^2}{4mM}$ is the Kantorovich constant.