Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-20T14:04:24.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Orlicz–Pettis Theorem for λ-multiplier convergent operator series

Published online by Cambridge University Press:  17 April 2009

Tao Yuanhong  and
Li Ronglu
Tao Yuanhong
Affiliation:
Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, Peoples Republic of China
Li Ronglu
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150006, Peoples Republic of China
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the λ-multiplier convergence of operator series depends completely upon the AK property of the sequence space λ, and thus present a lot of new important theorems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 2 , April 2007 , pp. 247 - 252
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Boos, H., Staurt, C. and Swartz, C., ‘Gliding hump properties of matrix domains’, Anal. Math. 30 (2004), 243–257.CrossRefGoogle Scholar
[2]Garnier, H.G., Dewilde, M. and Schmets, J., (in French), Analyse fonctionnelle théorie constructive des espaces linéaires à semi-normes. Tome 1: Théorie général (Birkhauser, Basel, 1968).Google Scholar
[3]Li, R., Cui, C. and Cho, M., ‘An invariant with respect to all admissible (X, X′)-polar topologies (Chinese)’, Chinese Ann. Math. Ser. A 19 (1998), 289–294.Google Scholar
[4]Stuart, C. and Swartz, C., ‘Generalization of the Orlicz–Pettis Theorems’, Proyecciones 24 (2005), 37–48.Google Scholar
[5]Swartz, C., Infinite matrices and the gliding hump (World Scientific Co., River Edge, N.J., 1996).CrossRefGoogle Scholar
[6]Swartz, C., ‘Orlicz–Pettis Theorems for multiplier convergent operator valued series’, Proyecciones 23 (2004), 61–72.Google Scholar
[7]Swartz, C. and Stuart, C., ‘Orlicz–Pettis Theorems for multiplier convergent’, Z. Anal. Anwendungen 17 (1998), 805–811.CrossRefGoogle Scholar
[8]Wen, S., Cui, C. and Li, R., ‘s-multiplier convergence and theorems of the Orlicz–Pettis-type’, Acta Math. Sinica (China) 43 (2000), 275–282.Google Scholar
[9]Wen, S., Jin, C., Cui, C. and Li, R., ‘s-multiplier convergence and its invariance for admissible polar topology’, J. Systems Sci. Math. Sci. (China) 20 (2000), 474–479.Google Scholar
[10]Wilansky, A., Modern methods in topological vector spaces (McGraw-Hill, New York, 1978).Google Scholar
[11]Wu, J. and Li, R., ‘An Orlicz–Pettis Theorem with applications to -spaces’, Studia Sci. Math. Hungar. 35 (1999), 353–358.Google Scholar
[12]Wu, J., Qu, W., and Cui, C., ‘On the invariant of λ-multiplier convergent series’, Adv. in Math. (China) 30 (2002), 279–283.Google Scholar
[13]Wu, J. and Lu, S., ‘A general Orlicz-Pettis Theorem’, Taiwanese J. Math. 6 (2002), 443–440.CrossRefGoogle Scholar