Unitarily invariant norm inequalities for elementary operators involving \(G_{1}\) operators (Q344884)

Studies on properties of elementary operators, \[R(X)=\sum_{i=1}^n A_iXB_i,\] with $A_i, B_i, X \in \mathbb{B}(\mathcal{H})$, have been of great concern for many mathematicians. In particular, the norm property has also been considered in a large number of papers but still it remains interesting to many mathematicians. Calculating these norms involves finding a formula that describes the norms of elementary operators in terms of their coefficients. However, results on norms have been obtained only in some special cases. NEWLINENEWLINEIn this paper, the authors obtain upper bounds for norms of some operators, more precisely $||| f(A)Xg(B)\pm X|||$ and $||| f(A)X\pm Xg(B)\pm X|||$ where $A, B$ and $X$ are operators, $||| . |||$ is a unitarily invariant norm and $f,g$ are certain analytic functions.