Local conjugacy theorems for \(C^1\) operators between Banach manifolds

Volume 9, Issue 3, pp 1341--1348 http://dx.doi.org/10.22436/jnsa.009.03.57

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1513 Downloads
• 2191 Views

Authors

Qiang Li - School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China. - School of Science, Qiqihar University, Qiqihar, 161006, P. R. China. Donghe Pei - School of Science, Qiqihar University, Qiqihar, 161006, P. R. China.

Abstract

In this paper, by the generalized inverse theory of bounded linear operators, the local conjugacy theorem for \(C^1\) operators between Banach manifolds is established. According to this theorem, the conditions which can be used to make sure that a \(C^1\) operator can be linearized are provided. Local conjugacy theorems for nonlinear Fredholm operators, nonlinear semi-Fredholm operators and finite rank operators are introduced.

Share and Cite

Keywords

• Conjugacy theorem
• generalized inverse
• linearization
• Banach manifold.

MSC

•  47A53
•  46T05
•  15A09

References

• [1] M. S. Berger, Nonlinearity and functional analysis, Academic Press, New York (1977)


• [2] N. Castro-González, J. Y. Vélez-Cerrada, On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces, J. Math. Anal. Appl., 341 (2008), 1213-1223.


• [3] C. Y. Deng, Y. M. Wei, New additive results for the generalized Drazin inverse, J. Math. Anal. Appl., 370 (2010), 313-321.


• [4] J. Ding , New perturbation results on pseudo-inverses of linear operators in Banach spaces, Linear Algebra Appl., 362 (2003), 229-235.


• [5] J. Ding, On the expression of generalized inverses of perturbed bounded linear operators, Missouri J. Math. Sci., 15 (2003), 40-47.


• [6] Q. L. Huang, W. X. Zhai , Perturbations and expressions for generalized inverses in Banach spaces and Moore-Penrose inverses in Hilbert spaces of closed linear operators, Linear Algebra Appl., 435 (2011), 117-127.


• [7] Q. L. Huang, L. P. Zhu, J. N. Yu, Some new perturbation results for generalized inverses of closed linear operators in Banach spaces, Banach J. Math. Anal., 6 (2012), 58-68.


• [8] P. Liu, Y. W. Wang, The best generalized inverse of the linear operator in normed linear space, Linear Algebra Appl., 420 (2007), 9-19.


• [9] J. P. Ma, (1-2) Inverses of operators between Banach spaces and local conjugacy theorem, Chinese Ann. Math. , 20 (1999), 57-62.


• [10] J. P. Ma , Complete rank theorem of advanced calculus and singularities of bounded linear operators, Front. Math. China., 3 (2008), 305-316.


• [11] M. Z. Nashed , Generalized inverses and applications, Academic Press, New York (1976)


• [12] P. Shi, J. P. Ma, A rank theorem for nonlinear semi-fredholm operators between two Banach manifolds, Acta Math. Sci., 26 (2006), 107-114.


• [13] E. Zeidler, Nonlinear functional analysis and its applications, IV, Applications to mathematical physics, Springer- Verlag, New York-Belin (1988)