1

Given a Banach space B，V is a subspace of B，if B/V is finite dimension，then is it enough to show that B is closed?

Thanks!

user48537
  • 871
  • 6
  • 14
  • 1
    See this question in MathOverflow – Mariano Suárez-Álvarez Apr 08 '14 at 04:02
  • Thanks for your comment and great reference. I need to think for a while. – user48537 Apr 08 '14 at 04:23
  • Thanks for your comment and great reference. I am sorry that the following question may be unclear. Is there concrete construction that the kernel can be described concretely? – user48537 Apr 08 '14 at 04:50
  • Find any non-zero linear functional on an infinite dimensional Banach space which is not continuous. Doing that explicitly needs recourse to the axiom of choice. See http://math.stackexchange.com/questions/99206/discontinuous-linear-functional and http://mathoverflow.net/questions/31163/unbounded-linear-operator-defined-on-l2/ – Mariano Suárez-Álvarez Apr 08 '14 at 04:53

0 Answers0