info:eu-repo/semantics/article
Some operator inequalities for unitary invariant norms
Fecha
2005-12Registro en:
Cano, Cristina; Mosconi, Irene; Stojanoff, Demetrio; Some operator inequalities for unitary invariant norms; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 46; 2; 12-2005; 53-66
0041-6932
1669-9637
CONICET Digital
CONICET
Autor
Cano, Cristina
Mosconi, Irene
Stojanoff, Demetrio
Resumen
Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitary invariant norm defined on a norm ideal I ⊆ L(H)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], we show that N(PTQ^{-1} +P^{-1}TQ + kT) (2+k) N(T), T ∈ I. This extends Zhang's inequality for matrices. We prove that this inequality is equivalent to two particular cases of itself, namely P=Q and Q=P^{-1}. We also characterize those numbers k such that the map ϒ : L(H)→ L(H) given by ϒ (T) = PTQ^{-1} +P^{-1}TQ + kT is invertible, and we estimate the induced norm of ϒ^{-1} acting on the norm ideal I. We compute sharp constants for the involved inequalities in several particular cases.