We present a Bellman inequality involving operator means for

operators acting on a Hilbert space. We also give some Bellman

inequalities concerning sesquilinear forms. Finally, we refine the

Jensen's ...

We investigate positive definite solutions of nonlinear matrix equations $X-f(\\Phi(X))=Q$ and $X-\\sum_{i=1}^{m}f(\\Phi_i(X))=Q$, where $Q$ is a positive definite matrix, $\\Phi$ and $\\Phi_i ~~(1\\leq i\\leq m)$ are ...

In this paper we investigate a notion, related to $f$-divergence functional, of relative operator

entropy, which develops the theory started by J.I. Fujii and E.

Kamei [Math. Japonica 34 (1989), 341--348]. ...

Let $A,B$ and $C$ be adjointable operators on a Hilbert $C^*$-module $\\mathscr{E}$. Giving a suitable version of the celebrated Douglas theorem in the context of Hilbert $C^*$-modules, we present the general solution of ...