User talk:Liuyipei
Welcome![edit]
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 Wikipedia:Questions, ask me on my talk page, or place {{helpme}} 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)
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.