On Antosik’s Lemma and the Antosik-Mikusinski Basic Matrix Theorem
HTML articles powered by AMS MathViewer
- by Qu Wenbo and Wu Junde PDF
- Proc. Amer. Math. Soc. 130 (2002), 3283-3285 Request permission
Abstract:
That Antosik’s Lemma is not a special case of the Antosik-Mikusinski Basic Matrix Theorem will be shown and, an equivalent form of the Antosik-Mikusinski Basic Matrix Theorem will also be presented in this paper.References
- Piotr Antosik and Charles Swartz, Matrix methods in analysis, Lecture Notes in Mathematics, vol. 1113, Springer-Verlag, Berlin, 1985. MR 781343, DOI 10.1007/BFb0072264
- Piotr Antosik, A lemma on matrices and its applications, Geometry of normed linear spaces (Urbana-Champaign, Ill., 1983) Contemp. Math., vol. 52, Amer. Math. Soc., Providence, RI, 1986, pp. 89–95. MR 840697, DOI 10.1090/conm/052/840697
- J. Wu and R. Li, An Orlicz-Pettis theorem with applications to $\scr A$-spaces, Studia Sci. Math. Hungar. 35 (1999), no. 3-4, 353–358. MR 1762248
- Junde Wu and Ronglu Li, Unconditional convergent series on locally convex spaces, Taiwanese J. Math. 4 (2000), no. 2, 253–259. MR 1757404, DOI 10.11650/twjm/1500407230
- J. Wu and R. Li, Hypocontinuity and uniform boundedness for bilinear maps, Studia Sci. Math. Hungar. 35 (1999), no. 1-2, 133–138. MR 1690248
- C. Swartz, Infinite matrices and the gliding hump, World Scientific Publishing Co., Inc., River Edge, NJ, 1996. MR 1423136, DOI 10.1142/9789812830036
- Rong Lu Li and Min-Hyung Cho, A uniform convergence principle, J. Harbin Inst. Tech. 24 (1992), no. 3, 107–108. MR 1200136
- Hans Weber, A diagonal theorem. Answer to a question of Antosik, Bull. Polish Acad. Sci. Math. 41 (1993), no. 2, 95–102 (1994). MR 1414755
Additional Information
- Qu Wenbo
- Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150006, People’s Republic of China
- Wu Junde
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Email: WJD@math.zju.edu.cn
- Received by editor(s): June 20, 2000
- Received by editor(s) in revised form: June 11, 2001
- Published electronically: May 29, 2002
- Additional Notes: This work was supported by the NSF of China
- Communicated by: Jonathan M. Borwein
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3283-3285
- MSC (2000): Primary 40C05
- DOI: https://doi.org/10.1090/S0002-9939-02-06475-4
- MathSciNet review: 1913007