DOI QR코드

DOI QR Code

DEMI-LINEAR ANALYSIS I-BASIC PRINCIPLES

  • Li, Ronglu (DEPARTMENT OF MATHEMATICS HARBIN INSTITUTE OF TECHNOLOGY) ;
  • Zhong, Shuhui (DEPARTMENT OF MATHEMATICS HARBIN INSTITUTE OF TECHNOLOGY) ;
  • Li, Linsong (DEPARTMENT OF MATHEMATICS YANBIAN UNIVERSITY)
  • Published : 2009.05.01

Abstract

The family of demi-linear mappings between topological vector spaces is a meaningful extension of the family of linear operators. We establish equicontinuity results for demi-linear mappings and develop the usual theory of distributions and the usual duality theory.

Keywords

References

  1. J. L. Kelley, General Topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955
  2. G. Kothe, Topological Vector Spaces I, Springer-Verlag New York Inc., New York, 1969
  3. R. Li, J. Chung, and D. Kim, Demi-distributions, to appear
  4. R. Li and C. Swartz, Spaces for which the uniform boundedness principle holds, Studia Sci. Math. Hungar. 27 (1992), no. 3-4, 379–384
  5. R. Li, S. Wen, and L. Li, Demi-linear analysis IV, to appear
  6. R. Li and S. Zhong, A new open mapping theorem, to appear
  7. J. Liu and Y. Luo, A resonance theorem for a family of $\alpha$-convex functionals, J. Math. Res. Exposition 19 (1999), no. 1, 103–107
  8. O. Naguard, A strong boundedness principle in Banach spaces, Proc. Amer. Math. Soc. 129 (2000), 861–863 https://doi.org/10.1090/S0002-9939-00-05607-0
  9. W. Roth, A uniform boundedness theorem for locally convex cones, Proc. Amer. Math. Soc. 126 (1998), 1973–1982
  10. C. Swartz, The evolution of the uniform boundedness principle, Math. Chronicle 19 (1990), 1–18
  11. C. Swartz, A uniform boundedness principle of Pt´ak, Comment. Math. Univ. Carolin. 34 (1993), no. 1, 149–151
  12. C. Swartz, Infinite Matrices and the Gliding Hump, World Scientific Publishing Co., Inc., River Edge, NJ, 1996
  13. A. Wilansky, Topology for Analysis, John Wiley, 1970
  14. A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill International Book Co., New York, 1978
  15. S. Zhong and R. Li, Continuity of mappings between Fr´echet spaces, J. Math. Anal. Appl. 311 (2005), no. 2, 736–743 https://doi.org/10.1016/j.jmaa.2005.03.060

Cited by

  1. Matrix transformations of l q (X) to l p (Y) vol.27, pp.1, 2012, https://doi.org/10.1007/s11766-012-2753-7
  2. Arzela-Ascoli Theorem for Demi-Linear Mappings vol.2014, 2014, https://doi.org/10.1155/2014/679825
  3. Demi-linear duality vol.2011, pp.1, 2011, https://doi.org/10.1186/1029-242X-2011-128