Irene Mosconi - Academia.edu (original) (raw)

Papers by Irene Mosconi

Revista De La Union Matematica Argentina, 2012

The aim of this paper is to relate the star order in operators in a Hilbert space with certain no... more The aim of this paper is to relate the star order in operators in a Hilbert space with certain norm inequalities. We are showing inequalities of the type BXA 2 ≤ XBA 2 (or BXA 2 ≥ XBA 2), which are already known under the assumption that A = ψ(B), with ψ a positive increasing (or decreasing, respectively) function defined on the spectrum of B. In this work, we will study this type of inequalities with the hypothesis that A ≤ * B, where A ≤ * B if A

Revista De La Union Matematica Argentina, 2012

The aim of this paper is to relate the star order in operators in a Hilbert space with certain no... more The aim of this paper is to relate the star order in operators in a Hilbert space with certain norm inequalities. We are showing inequalities of the type ‖BXA‖2 ≤ ‖XBA‖2 (or ‖BXA2‖ ≥ ‖XBA‖2), which are already known under the assumption that A = ψ(B), with ψ a positive increasing (or decreasing, respectively) function defined on the spectrum of B. In this work, we will study this type of inequalities with the hypothesis that A ≤∗ B, where A ≤∗ B if A∗A = B∗A and AA∗ = BA∗.

Linear and Multilinear Algebra, 2010

We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present... more We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present a new interpretation of this order which allows to generalize to this setting many known results for matrices: functional calculus, semi lattice properties, shorted operators and orthogonal decompositions. We also show several properties for general Hilbert spaces regarding the star order and its relationship with the functional calculus and the polar decomposition, which were unknown even in the finite dimensional setting. We also study of the existence of strong limits for star-monotone sequences and nets.

Mecanica Computacional

En este trabajo se presenta un problema de programaeion lineal que modela el proceso de operaeion... more En este trabajo se presenta un problema de programaeion lineal que modela el proceso de operaeion de la represa Alicura. Se justifiean las razones tecnicas y matematicas para eonsiderar el emprendimiento como un sistema aislado. Aspectos referentes a la obtencion y adecuacion de los datos son descriptos. La solucion se obtuvo usando el Metodo Simplex. Se hace referencia al problema dual, su interpretacion economica y analisis de sensibilidad. Finalmente, se hacen consideraciones sobre la funcion objetivo que Ilevan a una fOTmulacionno lineal y se resuelve usando la estrategia de programacion secuencial cuadratica. Se concluyen sobre aspectos referentes al modelo y alas implementaciones realizadas.

Annals of Functional Analysis

Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a u... more Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitarily 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`P T Q −1 + P −1 T Q + 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 ) = P T Q −1 + P −1 T Q + 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. *

Revista De La Union Matematica Argentina, 2012

The aim of this paper is to relate the star order in operators in a Hilbert space with certain no... more The aim of this paper is to relate the star order in operators in a Hilbert space with certain norm inequalities. We are showing inequalities of the type BXA 2 ≤ XBA 2 (or BXA 2 ≥ XBA 2), which are already known under the assumption that A = ψ(B), with ψ a positive increasing (or decreasing, respectively) function defined on the spectrum of B. In this work, we will study this type of inequalities with the hypothesis that A ≤ * B, where A ≤ * B if A

Revista De La Union Matematica Argentina, 2012

The aim of this paper is to relate the star order in operators in a Hilbert space with certain no... more The aim of this paper is to relate the star order in operators in a Hilbert space with certain norm inequalities. We are showing inequalities of the type ‖BXA‖2 ≤ ‖XBA‖2 (or ‖BXA2‖ ≥ ‖XBA‖2), which are already known under the assumption that A = ψ(B), with ψ a positive increasing (or decreasing, respectively) function defined on the spectrum of B. In this work, we will study this type of inequalities with the hypothesis that A ≤∗ B, where A ≤∗ B if A∗A = B∗A and AA∗ = BA∗.

Linear and Multilinear Algebra, 2010

We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present... more We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present a new interpretation of this order which allows to generalize to this setting many known results for matrices: functional calculus, semi lattice properties, shorted operators and orthogonal decompositions. We also show several properties for general Hilbert spaces regarding the star order and its relationship with the functional calculus and the polar decomposition, which were unknown even in the finite dimensional setting. We also study of the existence of strong limits for star-monotone sequences and nets.

Mecanica Computacional

En este trabajo se presenta un problema de programaeion lineal que modela el proceso de operaeion... more En este trabajo se presenta un problema de programaeion lineal que modela el proceso de operaeion de la represa Alicura. Se justifiean las razones tecnicas y matematicas para eonsiderar el emprendimiento como un sistema aislado. Aspectos referentes a la obtencion y adecuacion de los datos son descriptos. La solucion se obtuvo usando el Metodo Simplex. Se hace referencia al problema dual, su interpretacion economica y analisis de sensibilidad. Finalmente, se hacen consideraciones sobre la funcion objetivo que Ilevan a una fOTmulacionno lineal y se resuelve usando la estrategia de programacion secuencial cuadratica. Se concluyen sobre aspectos referentes al modelo y alas implementaciones realizadas.

Annals of Functional Analysis

Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a u... more Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitarily 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`P T Q −1 + P −1 T Q + 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 ) = P T Q −1 + P −1 T Q + 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. *