View More View Less
  • 1 Harbin Engineering University Department of Mathematics Harbin 150001 China
  • 2 Harbin Institute of Technology Department of Mathematics Harbin 150001 China
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

The concept of absolute convergence for series is generalized to locally convex spaces and an invariant theorem for absolutely convergent series in duality is established: when a locally convex space X is weakly sequentially complete, an admissible topology which is strictly stronger than the weak topology on X in the dual pair ( X,X′ ) is given such that it has the same absolutely convergent series as the weak topology in X .

  • Antosik, P. and Swartz, C. , Matrix Methods in Analysis , Lecture Notes in Math., 1113, Springer-Verlag, 1985. MR 87b :46079

  • Dvoretzky, A. and Rogers, C. A. , Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci., U.S.A. , 36 (1950), 192–197. MR 11 ,525a

    Rogers C. A. , 'Absolute and unconditional convergence in normed linear spaces ' (1950 ) 36 Proc. Nat. Acad. Sci., U.S.A. : 192 -197.

    • Search Google Scholar
  • Ronglu, Li, Longsuo, Li and Shin Min, Kang , Invariants in duality, Indian J. Pure appl. Math. , 33 (2002), no. 2, 171–183. MR 2003c :46010

    Shin Min K. , 'Invariants in duality ' (2002 ) 33 Indian J. Pure appl. Math. : 171 -183.

  • Ronglu, Li and Qingying, Bu , Locally convex spaces containing no copy of c 0 , J. Math. Anal. Appl. , 172 (1993), no. 1, 205–211. MR 94a :46002

    Qingying B. , 'Locally convex spaces containing no copy of c0 ' (1993 ) 172 J. Math. Anal. Appl. : 205 -211.

    • Search Google Scholar
  • Ronglu, Li, Yunyan, Y. and Swartz, C. , A general Orlicz-Pettis theorem, Studia Sci. Math. Hung. , 43 (2006), no. 1, 47–60. MR 2007b :46013

    Swartz C. , 'A general Orlicz-Pettis theorem ' (2006 ) 43 Studia Sci. Math. Hung. : 47 -60.

  • Rolewicz, S. , Metric Linear Spaces , Polish Sci. Publ., Warsaw, 1984. MR 88i :46004a

    Rolewicz S. , '', in Metric Linear Spaces , (1984 ) -.

  • Swartz, C. and Stuart, C. , Orlicz-Pettis theorems for multiplier convergent series, J. Anal. Appl. , 17 (1998), no. 4, 805–811. MR 2000i :46002

    Stuart C. , 'Orlicz-Pettis theorems for multiplier convergent series ' (1998 ) 17 J. Anal. Appl. : 805 -811.

    • Search Google Scholar
  • Wilansky, A. , Modern Methods in Topological Vector Spaces , McGraw-Hill, 1978. MR 81d :46001