S superpickleboy Mar 2010 19 0 May 10, 2010 #1 The question is if the sequence (vn) n belong to the natural numbers N whose linear span is the Hilbert space H, then H is finite dimensional. These sorts of proofs always confuse me. Thanks for any help given

The question is if the sequence (vn) n belong to the natural numbers N whose linear span is the Hilbert space H, then H is finite dimensional. These sorts of proofs always confuse me. Thanks for any help given

J Jose27 MHF Hall of Honor Apr 2009 721 310 México May 10, 2010 #2 superpickleboy said: The question is if the sequence (vn) n belong to the natural numbers N whose linear span is the Hilbert space H, then H is finite dimensional. These sorts of proofs always confuse me. Thanks for any help given Click to expand... Just use the Baire category theorem, with the sets \(\displaystyle A_k = span \{ v_1,...,v_k\}\) Last edited: May 10, 2010

superpickleboy said: The question is if the sequence (vn) n belong to the natural numbers N whose linear span is the Hilbert space H, then H is finite dimensional. These sorts of proofs always confuse me. Thanks for any help given Click to expand... Just use the Baire category theorem, with the sets \(\displaystyle A_k = span \{ v_1,...,v_k\}\)

S superpickleboy Mar 2010 19 0 May 11, 2010 #3 Jose27 said: Just use the Baire category theorem, with the sets \(\displaystyle A_k = span \{ v_1,...,v_k\}\) Click to expand... Never heard of that theorem before. Is there any other approach to it without the use of that theorem ?

Jose27 said: Just use the Baire category theorem, with the sets \(\displaystyle A_k = span \{ v_1,...,v_k\}\) Click to expand... Never heard of that theorem before. Is there any other approach to it without the use of that theorem ?