separable Hilbert space

From: "David Macmanus" <macmanus@xxxxxxxxxx>
Date: Sun, 21 Aug 2005 21:38:16 +0000 (UTC)

Can anyone give an example of a Hilbert space that isn't separable?
Separable Hilbert spaces have orthonormal bases which are either finite
or infinite, but countable. So I guess I'm wondering what's a space that
has an uncountable basis set of vectors.
Thanks,
David.

--
Posted via Mailgate.ORG Server - http://www.Mailgate.ORG
.

Follow-Ups:
- Re: separable Hilbert space
  - From: J. Horta
- Re: separable Hilbert space
  - From: Schoenfeld
- Re: separable Hilbert space
  - From: michaeld

Prev by Date: Re: This is absoluut fantastic, did Einstein see e=m.c^2 already in 1924?
Next by Date: Re: John Bahcall dies (Aug 18)
Previous by thread: Neumaier's Modification of Heisenberg Uncertainty Principle (HUP)
Next by thread: Re: separable Hilbert space
Index(es):
- Date
- Thread

Relevant Pages

Re: separable Hilbert space
... David Macmanus wrote: ... > Can anyone give an example of a Hilbert space that isn't separable? ... > Separable Hilbert spaces have orthonormal bases which are either finite ... Note that this sum is well defined - it is absolutely convergent by the ...
(sci.physics)
Re: separable Hilbert space
... >> Can anyone give an example of a Hilbert space that isn't separable? ... >> Separable Hilbert spaces have orthonormal bases which are either finite ... Dirac delta function and all that. ...
(sci.physics)
Re: separable Hilbert space
... > David Macmanus wrote: ... >> Can anyone give an example of a Hilbert space that isn't separable? ... >> Separable Hilbert spaces have orthonormal bases which are either finite ...
(sci.physics)
Re: separable Hilbert space
... > Can anyone give an example of a Hilbert space that isn't separable? ... > Separable Hilbert spaces have orthonormal bases which are either finite ... > or infinite, but countable. ...
(sci.physics)
Re: separable Hilbert space
... David Macmanus wrote: ... > Can anyone give an example of a Hilbert space that isn't separable? ... > Separable Hilbert spaces have orthonormal bases which are either finite ...
(sci.physics)