Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Banach spaces with the $ 4.3.$ intersection property

Author: Ȧsvald Lima
Journal: Proc. Amer. Math. Soc. 80 (1980), 431-434
MSC: Primary 46B05; Secondary 52A35
MathSciNet review: 580998
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that a finite-dimensional Banach space has the 4.3. intersection property if and only if it is isometric to an $ {l_\infty }$-sum of one- and two-dimensional spaces.

References [Enhancements On Off] (What's this?)

  • [1] Å. Lima, Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1-62. MR 0430747 (55:3752)
  • [2] -, Complex Banach spaces whose duals are $ {L_1}$-spaces, Israel J. Math. 24 (1976), 59-72. MR 0425584 (54:13538)
  • [3] -, An application of a theorem of Hirsberg and Lazar, Math. Scand. 38 (1976), 325-340. MR 0435802 (55:8758)
  • [4] J. Lindenstrauss, Extensions of compact operators, Mem. Amer. Math. Soc. No. 48 (1964). MR 0179580 (31:3828)
  • [5] E. Helly, Über Mengen konvexer Körper mit gemeinschaftlichen Punkten, Jber. Deutsch. Math.-Verein. 32 (1923), 175-176.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B05, 52A35

Retrieve articles in all journals with MSC: 46B05, 52A35

Additional Information

Keywords: n. k. intersection property, L-summands
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society