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2005 | 3 | 4 | 705-717
Tytuł artykułu

The geometry of Kato Grassmannians

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
4
Strony
705-717
Opis fizyczny
Daty
wydano
2005-12-01
online
2005-12-01
Twórcy
  • Polish Academy of Sciences
Bibliografia
  • [1] P. Abbondandolo and P. Majer: “Morse homology on Hilbert spaces”, Comm. Pure Applied Math., Vol. 54, (2001), pp. 689–760. http://dx.doi.org/10.1002/cpa.1012
  • [2] J. Avron, R. Seiler and B. Simon: “The index of a pair of projections”, J. Func. Anal., Vol. 120, (1994), pp. 220–237. http://dx.doi.org/10.1006/jfan.1994.1031
  • [3] B. Bojarski: “Abstract linear conjugation problems and Fredholm pairs of subspaces” (Russian), In: Differential and Integral equations, Boundary value problems. Collection of papers dedicated to the memory of Academician I, Vekua, Tbilisi University Press, Tbilisi, 1979, pp. 45–60.
  • [4] B. Bojarski: “Some analytical and geometrical aspects of the Riemann-Hilbert transmission problem”, In: Complex analysis. Methods, trends, applications, Akad. Verlag, Berlin, 1983, pp. 97–110.
  • [5] B. Bojarski: “The geometry of the Riemann-Hilbert problem”, Contemp. Math., Vol. 242, (1999), pp. 25–33.
  • [6] B. Bojarski: “The geometry of Riemann-Hilbert problem II”, In: Boundary value problems and integral equations. World Scientific, Singapore, 2000, pp. 41–48.
  • [7] B. Bojarski and G. Khimshiashvili: “Global geometric aspects of Riemann-Hilbert problems”, Georgian Math. J., Vol. 8 (2001), pp. 799–812.
  • [8] B. Bojarski and A. Weber: “Generalized Riemann-Hilbert transmission and boundary value problems. Fredholm pairs and bordisms”, Bull. Polish Acad. Sci., Vol. 50, (2002), pp. 479–496.
  • [9] B. Booss and K. Wojciechowsky: Elliptic boundary value problems for Dirac operators, Birkhäuser, Boston, 1993.
  • [10] M. Dupré and J. Glazebrook: “The Stiefel bundle of a Banach algebra”, Integr. Eq. Oper. Theory, Vol. 41, (2000), pp. 264–287. http://dx.doi.org/10.1007/BF01203172
  • [11] J. Eells: “Fredholm structures” Proc. Symp. Pure Math., Vol. 18, (1970), pp. 62–85.
  • [12] J. Elworthy and A. Tromba: “Differential structures and Fredholm maps on Banach manifolds”, Proc. Symp. Pure Math., Vol. 15, (1970), pp. 45–94.
  • [13] D. Freed: “The geometry of loop goups”, J. Diff Geom., Vol. 28, (1988), pp. 223–276.
  • [14] D. Freed: “An index theorem for families of Fredholm operators parametrized by a group”, Topology, Vol. 27, (1988), pp. 279–300. http://dx.doi.org/10.1016/0040-9383(88)90010-9
  • [15] T. Kato: Perturbation theory for linear operators, Springer, Berlin 1980.
  • [16] G. Khimshiashvili: On the topology of invertible linear singular integral operators, Springer Lecture Notes Math., Vol. 1214, (1986), pp. 211–230.
  • [17] G. Khimshiashvili: On Fredholmian aspects of linear conjugation problems, Springer Lect. Notes Math., Vol. 1520, (1992), pp. 193–216. http://dx.doi.org/10.1007/BFb0084722
  • [18] G. Khimshiashvili: “Homotopy classes of elliptic transmision problems over C *-algebras”, Georgian Math. J., Vol. 5, (1998), pp. 453–468. http://dx.doi.org/10.1023/B:GEOR.0000008116.53411.d0
  • [19] G. Khimshiashvili: “Geometric aspects of Riemann-Hilbert problems”, Mem. Diff. Eq. Math. Phys., Vol. 27, (2002), pp. 1–114.
  • [20] G. Khimshiashvili: “Global geometric aspects of linear conjugation problems”, J. Math. Sci., Vol. 118, (2003), pp. 5400–5466. http://dx.doi.org/10.1023/A:1025884428386
  • [21] A. Pressley and G. Segal: Loop groups, Clarendon Press, Oxford, 1986.
  • [22] K. Wojciechowski: “Spectral flow and the general linear conjugation problem”, Simon Stevin Univ. J., Vol. 59, (1985), pp. 59–91.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475627
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