Resumen de Tensorial and Hadamard product inequalities for functions of selfadjoint operators in Hilbert spaces in terms of Kantorovich ratio

Sever Silvestru Dragomir

• Let H be a Hilbert space. In this paper we show among others that, if f, g are continuous on the interval I with 0 <γ ≤ f(t)/g(t)≤ Γ for t ∈ I and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.