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Invariants in abstract mapping pairs

  • Li Ronglu (a1) and Wang Junming (a2)

Abstract

In a topological vector space, duality invariant is a very important property, some famous theorems, such as the Mackey-Arens theorem, the Mackey theorem, the Mazur theorem and the Orlicz-Pettis theorem, all show some duality invariants.

In this paper we would like to show an important improvement of the invariant results, which are related to sequential evaluation convergence of function series. Especially, a very general invariant result is established for an abstract mapping pair (Φ, B(Φ, X)) consisting of a nonempty set Φ and B(Φ, X) = {fXΦ: f (Φ) is bounded}, where X is a locally convex space.

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Copyright

References

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[1]Antosik, P., ‘A lemma on matrices and its applications’, Contemp. Math. 52 (1986), 8995.
[2]Dierolf, P., ‘Theorems of the Orlicz-Pettis type for locally convex spaces’, Manuscripta Math. 20 (1977), 7394.
[3]Khalleelulla, S. M., Counterexamples in topological vector spaces, Lecture Notes in Math. 935 (Springer, Heidelberg, 1982).
[4]Ronglu, Li, ‘Invariants on all admissible polar topologies’, Chinese Ann. Math. 19A (1998), 289290.
[5]Ronglu, Li, ‘The strongest Orlicz-Pettis topology’, Acta Math. Sinica 43 (2000), 916.
[6]Ronglu, Li and Qingying, Bu, ‘Locally convex spaces containing no copy of c0’, J. Math. Anal. Appl. 172 (1993), 205211.
[7]Ronglu, Li, Longsuo, Li and Minkang, Shin, ‘Summability results for operator matrices on topological vector spaces’, Science in China (A) 44 (2001), 13001311.
[8]Swartz, C., ‘An abstract Orlicz-Pettis theorem’, Bull. Acad. Polon. Sci. 32 (1984), 433437.
[9]Swartz, C., ‘A generalization of Mackey's theorem and the uniform boundedness principle’, Bull. Austral. Math. Soc. 40 (1989), 123128.
[10]Swartz, C., An introduction to functional analysis, Pure and Appl. Math. 157 (New York, 1992).
[11]Swartz, C., Infinite matrices and the gliding hump (World Scientific, Singapore, 1996).
[12]Swartz, C., ‘Orlicz-Pettis theorems for multiplier convergent series’, J. Anal. Appl. 17 (1998), 805811.
[13]Thomas, G. E. F., ‘L'integration par: qrapport a une measure de Radon vectorielle’, Ann. Inst. Fourier 20 (1970), 55191.
[14]Songlong, Wen, ‘s-Multiplier convergence and theorems of the Orlicz-Pettis type’, Acta Math. Sinica 43 (2000), 275282.
[15]Junde, Wu, ‘An Orlicz-Pettis theorem with application to A-spaces’, Studia Sci. Math. Hungar. 35 (1999), 353358.
[16]Junde, Wu and Ronglu, Li, ‘An equivalent form of Antosik-Mikusiński basic matrix theorem’, Advances in Math. 28 (1999), 268.
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Invariants in abstract mapping pairs

  • Li Ronglu (a1) and Wang Junming (a2)

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