Acta mathematica scientia,Series B ›› 1994, Vol. 14 ›› Issue (4): 446-450.

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A J-CONVEX SUBSET WHICH IS NOT PSH-CONVEX

Bu Shangquan   

  1. Department of applied mathematics, Tsinghua University, Beijing 100084, China
  • Received:1992-07-03 Online:1994-12-25 Published:1994-12-25
  • Supported by:
    Supported by the National Science Foundation of China.

Abstract: In this paper, we show that J-convex and PSH-convex are different notions for closed bounded subsets in complex Banach space. Precisely, we show that a complex Banach space X is infinite dimensional if and only if there exists a closed bounded J-convex subset which is not PSH-convex.

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