Generalized Schur complements and P-complementable operators

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Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space script H sign. We say that A is P-complementable if A-μP≥0 holds for some μ∈R. In this case we define I P(A)=max{μ∈R:A-μP≥0}. As a tool for computing I P(A) we introduce a natural generalization of th...

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Autores principales: Massey, Pedro Gustavo, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2004
Materias:
Matemática
Completely positive maps
Hadamard product
Positive semidefinite operators
Shorted operator
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/84639
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-84639
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Completely positive maps
Hadamard product
Positive semidefinite operators
Shorted operator
spellingShingle Matemática
Completely positive maps
Hadamard product
Positive semidefinite operators
Shorted operator
Massey, Pedro Gustavo
Stojanoff, Demetrio
Generalized Schur complements and P-complementable operators
topic_facet Matemática
Completely positive maps
Hadamard product
Positive semidefinite operators
Shorted operator
description Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space script H sign. We say that A is P-complementable if A-μP≥0 holds for some μ∈R. In this case we define I P(A)=max{μ∈R:A-μP≥0}. As a tool for computing I P(A) we introduce a natural generalization of the Schur complement or shorted operator of A to script S sign=R(P), denoted by Σ(A,P). We give expressions and a characterization for I P(A) that generalize some known results for particular choices of P. We also study some aspects of the shorted operator Σ(A,P) for P-complementable A, under the hypothesis of compatibility of the pair (A,script S sign). We give some applications in the finite dimensional context.
format Articulo
Articulo
author Massey, Pedro Gustavo
Stojanoff, Demetrio
author_facet Massey, Pedro Gustavo
Stojanoff, Demetrio
author_sort Massey, Pedro Gustavo
title Generalized Schur complements and P-complementable operators
title_short Generalized Schur complements and P-complementable operators
title_full Generalized Schur complements and P-complementable operators
title_fullStr Generalized Schur complements and P-complementable operators
title_full_unstemmed Generalized Schur complements and P-complementable operators
title_sort generalized schur complements and p-complementable operators
publishDate 2004
url http://sedici.unlp.edu.ar/handle/10915/84639
work_keys_str_mv AT masseypedrogustavo generalizedschurcomplementsandpcomplementableoperators
AT stojanoffdemetrio generalizedschurcomplementsandpcomplementableoperators
bdutipo_str Repositorios
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