DEMI-LINEAR ANALYSIS I-BASIC PRINCIPLES

Title & Authors
DEMI-LINEAR ANALYSIS I-BASIC PRINCIPLES
Li, Ronglu; Zhong, Shuhui; Li, Linsong;

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
demi-linear mappings;weakly demi-linear mappings;equicontinuity;uniform boundedness;demi-distributions;demi-linear duality;
Language
English
Cited by
1.
Matrix transformations of l q (X) to l p (Y), Applied Mathematics-A Journal of Chinese Universities, 2012, 27, 1, 78
2.
Arzela-Ascoli Theorem for Demi-Linear Mappings, Journal of Function Spaces, 2014, 2014, 1
3.
Demi-linear duality, Journal of Inequalities and Applications, 2011, 2011, 1, 128
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

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