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On Antosik's Lemma and the Antosik-Mikusinski Basic Matrix Theorem
Author(s):
Qu
Wenbo;
Wu
Junde
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3283-3285.
MSC (2000):
Primary 40C05
Posted:
May 29, 2002
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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:
-
- 1.
- P. Antosik, C. Swartz, Matrix Methods in Analysis, Lecture Notes in Mathematics, 1113, Springer-Verlag, Berlin, 1985. MR 87b:46079
- 2.
- P. Antosik, A lemma on matrices and its applications, Contemp. Math. 52(1986), 89-95. MR 87f:46022
- 3.
- Wu Junde, Li Ronglu, An Orlicz-Pettis theorem with applications to
 -spaces, Studia Sci. Math. Hungary. 35(1999), 353-358. MR 2001g:46004 - 4.
- Wu Junde, Li Ronglu, Unconditional convergent series on locally convex spaces, Taiwanese J. Math. (4)2000, 253-259. MR 2001b:46009
- 5.
- Wu Junde, Li Ronglu, Hypocontinuity and uniform boundedness for bilinear maps, Studia Sci. Math. Hungary. (35)1999, 133-138. MR 2000a:46003
- 6.
- C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, 1996. MR 98b:46002
- 7.
- Li Ronglu, Cho Minhyung, A uniform convergent principle, J. Harbin Institute of Technology 24(1992), 107-108. MR 94a:46016
- 8.
- H. Weber, A diagonal theorem. Answer to a question of Antosik, Bull. Polish Acad. Sci. Math., 41(1993), 95-102. MR 98c:22001
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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
DOI:
10.1090/S0002-9939-02-06475-4
PII:
S 0002-9939(02)06475-4
Keywords:
Antosik lemma,
basic matrix theorem,
uniform convergence principle
Received by editor(s):
June 20, 2000
Received by editor(s) in revised form:
June 11, 2001
Posted:
May 29, 2002
Additional Notes:
This work was supported by the NSF of China
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2002,
American Mathematical Society
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