Index of Hadamard multiplication by positive matrices II

• Autores: Corach, Gustavo; Stojanoff, Demetrio
• Año de publicación: 2001
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Ciencias Exactas; Matemática; 47A30; 47B15; Hadamard product; Norm inequalities; Positive semidefinite matrices
• Institución: Universidad Nacional de La Plata

For each n×n positive semidefinite matrix A we define the minimal index I(A)=max{λ≥0:A∘B≥λB for all B≥0} and, for each norm N, the N-index I_N(A)=min{N(A∘B):B≥0 and N(B)=1}, where A ∘ B=[a_ijb_ij] is the Hadamard or Schur product of A=[a_ij] and B=[b_ij] and B≥0 means that B is a positive semidefinite matrix. A comparison between these indexes is done, for different choices of the norm N. As an application we find, for each bounded invertible selfadjoint operator S on a Hilbert space, the best constant M(S) such that ∥STS+S^-1TS^-1∥≥M(S)∥T∥ for all T≥0.
Facultad de Ciencias Exactas