Reverses of Ando's inequality for positive linear maps

An Inequality for Linear Positive Functionals

Using P0-simple functionals, we generalise the result from Theorem 1.1 obtained by Professor F. Qi (F. QI, An algebraic inequality, RGMIA Res. Rep. Coll., 2(1) (1999), article 8).

Ela a Diaz–metcalf Type Inequality for Positive Linear Maps and Its Applications∗

We present a Diaz–Metcalf type operator inequality as a reverse Cauchy–Schwarz inequality and then apply it to get some operator versions of Pólya–Szegö’s, Greub–Rheinboldt’s, Kantorovich’s, Shisha–Mond’s, Schweitzer’s, Cassels’ and Klamkin–McLenaghan’s inequalities via a unified approach. We also give some operator Grüss type inequalities and an operator Ozeki– Izumino–Mori–Seo type inequality...

A Diaz-Metcalf type inequality for positive linear maps and its applications

We present a Diaz–Metcalf type operator inequality as a reverse Cauchy–Schwarz inequality and then apply it to get some operator versions of Pólya–Szegö’s, Greub–Rheinboldt’s, Kantorovich’s, Shisha–Mond’s, Schweitzer’s, Cassels’ and Klamkin–McLenaghan’s inequalities via a unified approach. We also give some operator Grüss type inequalities and an operator Ozeki– Izumino–Mori–Seo type inequality...

Asymptotic Lifts of Positive Linear Maps

We show that the notion of asymptotic lift generalizes naturally to normal positive maps φ : M → M acting on von Neumann algebras M . We focus on cases in which the domain of the asymptotic lift can be embedded as an operator subsystem M∞ ⊆ M , and characterize when M∞ is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of φ.

Positive Linear Maps and Spreads of Matrices