Abstract:
Given a closed subspace S of a Hilbert space H and a (bounded) selfadjoint operator B acting on H, a min-max representation of the shorted operator (or Schur complement) of B to S is obtained under compatibility hypotheses. Also, an extension of Pekarev's formula is given. © 2007 Elsevier Inc. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | Shorting selfadjoint operators in Hilbert spaces |
Autor: | Giribet, J.I.; Maestripieri, A.; Pería, F.M. |
Filiación: | Departamento de Matemática, FI-UBA, Buenos Aires, Argentina IAM-CONICET, Saavedra 15, Piso 3, 1083 Buenos Aires, Argentina Departamento de Matemática, FCE-UNLP, La Plata, Argentina
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Palabras clave: | Schur complement; Selfadjoint operator; Shorted operator; Mathematical operators; Numerical methods; Operations research; Schur complement; Selfadjoint operator; Shorted operator; Hilbert spaces |
Año: | 2008
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Volumen: | 428
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Número: | 8-9
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Página de inicio: | 1899
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Página de fin: | 1911
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DOI: |
http://dx.doi.org/10.1016/j.laa.2007.10.034 |
Título revista: | Linear Algebra and Its Applications
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Título revista abreviado: | Linear Algebra Its Appl
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ISSN: | 00243795
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CODEN: | LAAPA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v428_n8-9_p1899_Giribet |
Referencias:
- Albert, A., Conditions for positive and nonnegative definiteness in terms of pseudoinverses (1969) SIAM J. Appl. Math., 17 (2), pp. 434-440
- Anderson Jr., W.N., Trapp, G.E., Shorted operators II (1975) SIAM J. Appl. Math., 28, pp. 60-71
- Ando, T., Generalized Schur complements (1979) Linear Algebra Appl., 27, pp. 173-186
- Antezana, J., Corach, G., Stojanoff, D., Bilateral shorted operators and parallel sum (2006) Linear Algebra Appl., 414 (2-3), pp. 570-588
- Bouldin, R., The product of operators with closed range (1973) Tohoku Math. J., 25, pp. 359-363
- Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Studies in Applied Mathematics, , SIAM
- Corach, G., Maestripieri, A., Stojanoff, D., Oblique projections and Schur complements (2001) Acta Sci. Math. (Szeged), 67, pp. 256-337
- Corach, G., Maestripieri, A., Stojanoff, D., Generalized Schur complements and oblique projections (2002) Linear Algebra Appl., 341, pp. 259-272
- G. Corach, A. Maestripieri, D. Stojanoff, A classification of projectors, Banach Center Publication, Institute of Mathematics, Polish Academy of Sciences, Warszawa 67 (2004) 145-160; Dullerud, G.E., Paganini, F., (2000) A Course in Robust Control Theory, , Springer
- Hassi, S., Nordström, K., On projections in a space with an indefinite metric (1994) Linear Algebra Appl., 208-209, pp. 401-417
- Izumino, S., The product of operators with closed range and an extension of the reverse order law (1982) Tohoku Math. J., 34, pp. 43-52
- Krein, M., The theory of self-adjoint extensions of semibounded Hermitian operators and its applications (1947) Mat. Sb. (N.S.), 20 (62), pp. 431-495
- Maestripieri, A., Martínez Pería, F., Decomposition of selfadjoint projections in Krein spaces (2006) Acta Sci. Math., 72, pp. 611-638
- Massey, P., Stojanoff, D., Generalized Schur complements and P-complementable operators (2004) Linear Algebra Appl., 393, pp. 299-318
- Pekarev, E.L., Shorts of operators and some extremal problems (1992) Acta Sci. Math. (Szeged), 56, pp. 147-163
- Ju.L. Smul'jan, A Hellinger operator integral, (Russian) Mat. Sb. (N.S.) 49 (91) 1959 381-430; (English) Amer. Math. Soc. Translations 22 (1962) 289-337
Citas:
---------- APA ----------
Giribet, J.I., Maestripieri, A. & Pería, F.M.
(2008)
. Shorting selfadjoint operators in Hilbert spaces. Linear Algebra and Its Applications, 428(8-9), 1899-1911.
http://dx.doi.org/10.1016/j.laa.2007.10.034---------- CHICAGO ----------
Giribet, J.I., Maestripieri, A., Pería, F.M.
"Shorting selfadjoint operators in Hilbert spaces"
. Linear Algebra and Its Applications 428, no. 8-9
(2008) : 1899-1911.
http://dx.doi.org/10.1016/j.laa.2007.10.034---------- MLA ----------
Giribet, J.I., Maestripieri, A., Pería, F.M.
"Shorting selfadjoint operators in Hilbert spaces"
. Linear Algebra and Its Applications, vol. 428, no. 8-9, 2008, pp. 1899-1911.
http://dx.doi.org/10.1016/j.laa.2007.10.034---------- VANCOUVER ----------
Giribet, J.I., Maestripieri, A., Pería, F.M. Shorting selfadjoint operators in Hilbert spaces. Linear Algebra Its Appl. 2008;428(8-9):1899-1911.
http://dx.doi.org/10.1016/j.laa.2007.10.034