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Abstract:

Let CR be the set of all bounded linear operators between Hilbert spaces H, κ with closed range. This paper is devoted to the study of the topological properties of CR. if certain natural metrics are considered on it. We also define an action of the group GH × Gκ, on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR. © Copyright by THETA 2009.

Registro:

Documento: Artículo
Título:Metric and homogeneous structure of closed range operators
Autor:Corach, G.; Maestripieri, A.; Mbekhta, M.
Filiación:IAM-CONICET, Departamento de Matemática, UBA, Buenos Aires, 1063, Argentina
Département de Mathématiques, Université Lille 1, F-59655, France
Palabras clave:Closed range; Moore-Penrose inverse; Partial isometry; Positive operators, orbits; Semi-Fredholm operators
Año:2009
Volumen:61
Número:1
Página de inicio:171
Página de fin:190
Título revista:Journal of Operator Theory
Título revista abreviado:J. Oper. Theory
ISSN:03794024
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v61_n1_p171_Corach

Referencias:

  • ANDRUCHOW, E., CORACH, G., Differential geometry of partial isometries and partial unitaries (2004) Illinois J. Math, 48, pp. 97-120
  • ANDRUCHOW, E., CORACH, G., MBEKHTA, M., On the geometry of generalized inverses (2005) Math. Nachr, 278, pp. 756-770
  • ANDRUCHOW, E., CORACH, G., STOJANOFF, D., Projective spaces of a C*-algebra (2000) Integral Equations Operator Theory, 37, pp. 143-168
  • ATKIN, C.J., The Finsler geometry of groups of isometries of Hilbert space (1987) J. Austral. Math. Soc. Ser. A, 42, pp. 196-222
  • ATKIN, C.J., The Finsler geometry of certain covering groups of operator groups (1989) Hokkaido Math. J, 18, pp. 45-77
  • ATKINSON, F.V., On relatively regular operators (1953) Ada Sci. Math. (Szeged), 15, pp. 38-56
  • BEN-ISRAEL, A., GREVILLE, T.N.E., (2003) Generalized Inverses. Theory and Applications, , second edition, Springer-Verlag, New York
  • BOULDIN, R., The product of operators with closed range (1973) Tohoku Math. J. (2), 25, pp. 359-363
  • BOULDIN, R., Closed range and relative regularity for products (1977) J. Math. Anal. Appl, 61, pp. 397-403
  • BUCKHOLTZ, D., Hilbert space idempotents and involutions (2000) Proc. Amer. Math. Soc, 128, pp. 1415-1418
  • CARADUS, S.R., PFAFFENBERGER, W.E., YOOD, B., (1974) Calkin Algebras and Algebras of Operators on Banach Spaces, , Marcel Dekker, New York
  • CHEN, G., WEI, M., Perturbation analysis of the least squares solution in Hilbert spaces (1996) Linear Algebra Appl, 244, pp. 69-80
  • CORACH, G., Operator inequalities, geodesies and interpolation (1994) Functional Analysis and Operator Theory (Warsaw, 1992), 30, pp. 101-115. , Banach Center Publ, Polish Acad. Sci, Warsaw
  • CORACH, G., MAESTRIPIERI, A., Differential and metrical structure of positive operators (1999) Positivity, 3, pp. 297-315
  • CORACH, G., MAESTRIPIERI, A., STOJANOFF, D., Orbits of positive operators from a differentiable viewpoint (2004) Positivity, 8, pp. 31-48
  • CORACH, G., PORTA, H., RECHT, L., Differential geometry of spaces of relatively regular operators (1990) Integral Equations Operator Theory, 13, pp. 771-794
  • CORACH, G., PORTA, H., RECHT, L., Differential geometry of systems of projections in Banach algebras (1990) Pacific J. Math, 143, pp. 209-228
  • CORACH, G., PORTA, H., RECHT, L., The geometry of spaces of projections in C*-algebras (1993) Adv. in Math, 101, pp. 59-77
  • CORACH, G., PORTA, H., RECHT, L., The geometry of the spaces of selfadjoint invertible elements of a C*-algebra (1993) Integral Equations Operator Theory, 16, pp. 333-359
  • DEUTSCH, F., The angle between subspaces in Hilbert space (1995) Approximation Theory, Wavelets and Applications, pp. 107-130. , Kluwer, Netherlands
  • DING, J., HUANG, L.J., On the continuity of the pseudoinverse (1997) Linear Algebra Appl, 262, pp. 229-242
  • DIXMIER, J., Etudes sur les variétés et opérateurs de Julia, avec quelques applications (1949) Bull. Soc. Math. France, 77, pp. 11-101
  • J. DIXMIER, Sur les variétés J d'un espace de Hilbert, J. Math. Pures Appl. (9) 28(1949), 321-358; DOUGLAS, R.G., On majorization, factorization, and range inclusion of operators on Hilbert space (1966) Proc. Amer. Math. Soc, 17, pp. 413-115
  • FILLMORE, P.A., WILLIAMS, J.P., On operator ranges (1971) Adv. in Math, 7, pp. 254-281
  • GOLDBERG, S., (1985) Unbounded Operators, Theory and Applications, , Dover, New York
  • B. GRAMSCH, Relative Inversion in der Störungstheorie von Operatoren und ψ-Algebren, Math. Ann. 269(1984), 27-71; HALMOS, P.R., (1982) A Hilbert Space Problem Book, , 2nd. ed, Springer Verlag, New York
  • HALMOS, P.R., MCLAUGHLIN, J.E., Partial isometries (1963) Pacific J. Math, 13, pp. 585-596
  • HARTE, R., MBEKHTA, M., On generalized inverses in C*-algebras (1992) Studia Math, 103, pp. 71-77
  • HARTE, R., MBEKHTA, M., Generalized inverses in C*-algebras. II (1993) Studia Math, 106, pp. 129-138
  • IZUMINO, S., Convergence of generalized splines and spline projectors (1983) J. Approx. Theory, 38, pp. 269-278
  • KATO, T., (1976) Perturbation Theory for Linear Operators, , second edition, Springer-Verlag, Berlin-Heidelberg-New York
  • KUIPER, N., The homotopy type of the unitary group of Hilbert spaces (1965) Topology, 3, pp. 19-30
  • J.-P. LABROUSSE, M. MBEKHTA, Les opérateurs points de continuité pour la conorme et l'inverse de Moore-Penrose, Houston J. Math. 18(1992), 7-23; LANG, S., (2002) Introduction to Differentiate Manifolds, , second edition, Springer-Verlag, New York
  • MAESTRIPIERI, A., On the geometry of the set of square roots of elements in C*-algebras (1994) Integral Equations Operator Theory, 19, pp. 290-313
  • MBEKHTA, M., Résolvant généralisé et théorie spectrale (1989) J. Operator Theory, 21, pp. 69-105
  • MBEKHTA, M., Conorme et inverses généralisés dans les C*-algebres (1992) Cañad. Math. Bull, 35, pp. 515-522
  • MBEKHTA, M., Sur la structure des composantes connexes semi-Fredholm de B(H) (1992) Proc. Amer. Math. Soc, 116, pp. 521-524
  • MBEKHTA, M., On the stability of semi-Fredholm operators (1996) J. Operator Theory, 35, pp. 191-201
  • MBEKHTA, M., SKHIRI, H., Partial isometries: Factorization and connected components (2000) Integral Equations Operator Theory, 38, pp. 334-349
  • NUSSBAUM, R.D., Hilbert's projective metric and iterated nonlinear maps (1988) Mem. Amer. Math. Soc, 39, p. 1
  • PENROSE, R., A generalized inverse for matrices (1955) Proc. Cambridge Phil. Soc, 51, pp. 406-413
  • PENROSE, R., On best approximation solutions of linear matrix equations (1956) Proc. Cambridge Phil. Soc, 52, pp. 17-19
  • PORTA, H., RECHT, L., Minimality of geodesies in Grassmann manifolds (1987) Proc. Amer. Math. Soc, 100, pp. 464-466
  • RAEBURN, I., The relationship between a commutative Banach algebra and its maximal ideal space (1977) J. Funct. Anal, 25, pp. 366-390
  • REED, M., SIMON, B., (1972) Methods in Modern Mathematical Physics. Functional Analysis, , Academic Press, New York
  • SKHIRI, H., Structure of semi-Fredholm operators with fixed nullity (1997) Ada Sci. Math. (Szeged), 63, pp. 607-622
  • STEWART, G.W., On the perturbation of pseudo-inverses, projections, and linear least squares problems (1977) SIAM Rev, 19, pp. 634-662
  • THOMPSON, A.C., On certain contraction mappings in a partially ordered vector space (1963) Proc. Amer. Math. Soc, 14, pp. 438-443
  • WEDIN, P.-A., Perturbation theory for pseudo-inverses (1973) Nordisk Tidskr. Informationsbe-handling (BIT), 13, pp. 217-232

Citas:

---------- APA ----------
Corach, G., Maestripieri, A. & Mbekhta, M. (2009) . Metric and homogeneous structure of closed range operators. Journal of Operator Theory, 61(1), 171-190.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v61_n1_p171_Corach [ ]
---------- CHICAGO ----------
Corach, G., Maestripieri, A., Mbekhta, M. "Metric and homogeneous structure of closed range operators" . Journal of Operator Theory 61, no. 1 (2009) : 171-190.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v61_n1_p171_Corach [ ]
---------- MLA ----------
Corach, G., Maestripieri, A., Mbekhta, M. "Metric and homogeneous structure of closed range operators" . Journal of Operator Theory, vol. 61, no. 1, 2009, pp. 171-190.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v61_n1_p171_Corach [ ]
---------- VANCOUVER ----------
Corach, G., Maestripieri, A., Mbekhta, M. Metric and homogeneous structure of closed range operators. J. Oper. Theory. 2009;61(1):171-190.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v61_n1_p171_Corach [ ]