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Orlicz–Pettis Theorem for λ-multiplier convergent operator series

  • Tao Yuanhong (a1) and Li Ronglu (a2)

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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.

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References

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[1]Boos, H., Staurt, C. and Swartz, C., ‘Gliding hump properties of matrix domains’, Anal. Math. 30 (2004), 243257.
[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).
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[5]Swartz, C., Infinite matrices and the gliding hump (World Scientific Co., River Edge, N.J., 1996).
[6]Swartz, C., ‘Orlicz–Pettis Theorems for multiplier convergent operator valued series’, Proyecciones 23 (2004), 6172.
[7]Swartz, C. and Stuart, C., ‘Orlicz–Pettis Theorems for multiplier convergent’, Z. Anal. Anwendungen 17 (1998), 805811.
[8]Wen, S., Cui, C. and Li, R., ‘s-multiplier convergence and theorems of the Orlicz–Pettis-type’, Acta Math. Sinica (China) 43 (2000), 275282.
[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), 474479.
[10]Wilansky, A., Modern methods in topological vector spaces (McGraw-Hill, New York, 1978).
[11]Wu, J. and Li, R., ‘An Orlicz–Pettis Theorem with applications to -spaces’, Studia Sci. Math. Hungar. 35 (1999), 353358.
[12]Wu, J., Qu, W., and Cui, C., ‘On the invariant of λ-multiplier convergent series’, Adv. in Math. (China) 30 (2002), 279283.
[13]Wu, J. and Lu, S., ‘A general Orlicz-Pettis Theorem’, Taiwanese J. Math. 6 (2002), 443–440.
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Orlicz–Pettis Theorem for λ-multiplier convergent operator series

  • Tao Yuanhong (a1) and Li Ronglu (a2)

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