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On Antosik's Lemma and the Antosik-Mikusinski Basic Matrix Theorem


Authors: Qu Wenbo and Wu Junde
Journal: Proc. Amer. Math. Soc. 130 (2002), 3283-3285
MSC (2000): Primary 40C05
Published electronically: May 29, 2002
MathSciNet review: 1913007
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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.


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  • 1. Piotr Antosik and Charles Swartz, Matrix methods in analysis, Lecture Notes in Mathematics, vol. 1113, Springer-Verlag, Berlin, 1985. MR 781343
  • 2. 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, 10.1090/conm/052/840697
  • 3. J. Wu and R. Li, An Orlicz-Pettis theorem with applications to 𝒜-spaces, Studia Sci. Math. Hungar. 35 (1999), no. 3-4, 353–358. MR 1762248
  • 4. Junde Wu and Ronglu Li, Unconditional convergent series on locally convex spaces, Taiwanese J. Math. 4 (2000), no. 2, 253–259. MR 1757404
  • 5. 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
  • 6. C. Swartz, Infinite matrices and the gliding hump, World Scientific Publishing Co., Inc., River Edge, NJ, 1996. MR 1423136
  • 7. Rong Lu Li and Min-Hyung Cho, A uniform convergence principle, J. Harbin Inst. Tech. 24 (1992), no. 3, 107–108. MR 1200136
  • 8. 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

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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: https://doi.org/10.1090/S0002-9939-02-06475-4
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
Published electronically: May 29, 2002
Additional Notes: This work was supported by the NSF of China
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society