Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stupid Question

  1. Oct 23, 2011 #1
    I am sure that my questions are stupid. If we have a Hilbert space H, what do we mean by the closed subspace of H. Also, Does every Hilbert space have an identity? :P.

    Could any one please clean to me these things .
  2. jcsd
  3. Oct 23, 2011 #2
    A subspace of a vector space (and a Hilbert space is a vector space) is a nonempty set X such that

    • [itex]x,y\in X~\Rightarrow~x+y\in X[/itex]
    • [itex]x\in X,\alpha\in \mathbb{C}~\Rightarrow~\alpha x\in X[/itex]

    A Hilbert space also comes equipped with a norm:


    and a set X is closed under the norm if for all convergent sequences in X it holds that the limit is in X.

    A closed subspace is something that is both a subspace and closed.

    What do you mean with identity?? It has a 0, which is the additive identity...
  4. Oct 23, 2011 #3
    Thank You.
    I mean 1.
  5. Oct 23, 2011 #4
    That doesn't really help me. What is 1 supposed to mean??
  6. Oct 23, 2011 #5
    1 is the multiplicative identity
  7. Oct 23, 2011 #6
    And since when does a Hilbert space have a multiplication??
  8. Oct 23, 2011 #7
    Oops, thank you, that is why the question is stupid.
  9. Oct 23, 2011 #8
    There are no stupid questions :tongue2:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Stupid Question Date
Stupid questions of basic analysis Oct 13, 2010
Stupid questions from basic topology Oct 3, 2010
Stupid question Sep 29, 2010
Stupid Question Apr 1, 2008
Stupid Question, Curious Dec 14, 2004