User talk:Liuyipei

Welcome!
Hello Liuyipei, welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Our intro page contains a lot of helpful material for new users—please check it out! If you need help, visit Questions, ask me on my talk page, or place   on this page, followed by your question, and someone will show up shortly to answer your questions. Kiefer .Wolfowitz 10:35, 28 February 2012 (UTC)

Hilbert space
In infinite dimensions, an algebraic Hamel basis does not do much for analysis. A Schauder basis is more useful, but any Schauder basis (if one exists) has limitations for linear metric spaces.

Consider: A Banach space is a Hilbert space if and only if each of its closed subspaces has a closed complementary subspace (whose direct sum equals the whole space), a result of Lindenstrauss and Tzarafi, I believe, from the 1960s.

Kiefer .Wolfowitz 10:39, 28 February 2012 (UTC)