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2013 | 11 | 6 | 1004-1019
Tytuł artykułu

A note on the differentiable structure of generalized idempotents

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
6
Strony
1004-1019
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-03-28
Twórcy
Bibliografia
  • [1] Andruchow E., Corach G., Stojanoff D., Projective spaces of a C*-algebra, Integral Equations Operator Theory, 2000, 37(2), 143–168 http://dx.doi.org/10.1007/BF01192421[Crossref]
  • [2] Andruchow E., Stojanoff D., Nilpotent operators and systems of projections, J. Operator Theory, 1988, 20(2), 359–374
  • [3] Andruchow E., Stojanoff D., Differentiable structure of similarity orbits, J. Operator Theory, 1989, 21(2), 349–366
  • [4] Baksalary J.K., Baksalary O.M., Liu X., Further properties of generalized and hypergeneralized projectors, Linear Algebra Appl., 2004, 389, 295–303 http://dx.doi.org/10.1016/j.laa.2004.03.013[WoS][Crossref]
  • [5] Baksalary J.K., Baksalary O.M., Liu X., Trenkler G., Further results on generalized and hypergeneralized projectors, Linear Algebra Appl., 2008, 429(5–6), 1038–1050 http://dx.doi.org/10.1016/j.laa.2007.03.029[Crossref][WoS]
  • [6] Baksalary J.K., Liu X., An alternative characterization of generalized projectors, Linear Algebra Appl., 2004, 388, 61–65 http://dx.doi.org/10.1016/j.laa.2004.01.010[Crossref]
  • [7] Beltiţă D., Smooth Homogeneous Structures in Operator Theory, Chapman Hall/CRC Monogr. Surv. Pure Appl. Math., 137, Chapman & Hall/CRC, Boca Raton, 2006
  • [8] Benítez J., Thome N., Characterizations and linear combinations of k-generalized projectors, Linear Algebra Appl., 2005, 410, 150–159 http://dx.doi.org/10.1016/j.laa.2005.03.007[Crossref]
  • [9] Corach G., Porta H., Recht L., Differential geometry of systems of projections in Banach algebras, Pacific J. Math., 1990, 143(2), 209–228 http://dx.doi.org/10.2140/pjm.1990.143.209[Crossref]
  • [10] Corach G., Porta H., Recht L., The geometry of spaces of projections in C*-algebras, Adv. Math., 1993, 101(1), 59–77 http://dx.doi.org/10.1006/aima.1993.1041[Crossref]
  • [11] Davis C., Kahan W.M., Weinberger H.F., Norm preserving dilations and their applications to optimal error bounds, SIAM J. Numer. Anal., 1982, 19(3), 445–469 http://dx.doi.org/10.1137/0719029[Crossref]
  • [12] Du H.-K., Li Y., The spectral characterization of generalized projections, Linear Algebra Appl., 2005, 400, 313–318 http://dx.doi.org/10.1016/j.laa.2004.11.027[Crossref]
  • [13] Du H.-K., Wang W.-F., Duan Y.-T., Path connectivity of k-generalized projectors, Linear Algebra Appl., 2007, 422(2–3), 712–720 http://dx.doi.org/10.1016/j.laa.2006.12.001[Crossref][WoS]
  • [14] Groß J., Trenkler G., Generalized and hypergeneralized projectors, Linear Algebra Appl., 1997, 264, 463–474 http://dx.doi.org/10.1016/S0024-3795(96)00541-1[Crossref]
  • [15] Herrero D.A., Approximation of Hilbert Space Operators, I, 2nd ed., Pitman Res. Notes Math. Ser., 224, Longman Scientific & Technical, Harlow; John Wiley & Sons, New York, 1989
  • [16] Kovarik Z.V., Manifolds of frames of projectors, Linear Algebra Appl., 1980, 31, 151–158 http://dx.doi.org/10.1016/0024-3795(80)90215-3[Crossref]
  • [17] Kovarik Z.V., Sherif N., Characterization of similarities between two n-frames of projectors, Linear Algebra Appl., 1984, 57, 57–69 http://dx.doi.org/10.1016/0024-3795(84)90176-9[Crossref]
  • [18] Kovarik Z.V., Sherif N., Geodesics and near-geodesics in the manifolds of projector frames, Linear Algebra Appl., 1988, 99, 259–277 http://dx.doi.org/10.1016/0024-3795(88)90136-X[Crossref]
  • [19] Lebtahi L., Thome N., A note on k-generalized projections, Linear Algebra Appl., 2007, 420(2–3), 572–575 http://dx.doi.org/10.1016/j.laa.2006.08.011[Crossref]
  • [20] Porta H., Recht L., Minimality of geodesics in Grassmann manifolds, Proc. Amer. Math. Soc., 1987, 100(3), 464–466 http://dx.doi.org/10.1090/S0002-9939-1987-0891146-6[Crossref]
  • [21] Stewart G.W., A note on generalized and hypergeneralized projectors, Linear Algebra Appl., 2006, 412(2–3), 408–411 http://dx.doi.org/10.1016/j.laa.2005.07.022[Crossref]
Typ dokumentu
Bibliografia
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