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In some applications that I have seen, one needs to consider both a vector space V, its dual space, its complex conjugate space, and even the dual of the complex conjugate space. In this case, a notation which distinguishes the dual space from the complex conjugate space is needed. In the current article, the same notation is used for the complex conjugate space (a star sign) as is used for the dual space in its article. Suggestion: either change the notation to distinguish it from the dual space, or explain that sometimes different notations are needed.
I lack a good motivation for the introduction of the complex conjugate space. I am not an expert in this field myself and have no suggestion, but I guess that there are some in physics?
I get the feeling that the current article is a mix between basic facts, such as how a complex conjugate space is constructed, and advanced material such as functors and categories. I doubt that many who reads about complex conjugate spaces for the first time here have any idea what functors and categories are. I will try to make a separation of the two types of information.
I changed all the stars to overlines. Since I don't know how to make overlines on normalsize letters, all math symbols are now in larger font, hope that's OK. (The stars didn't look very good, either.) I added one sentence of motivation.--345Kai (talk) 09:37, 21 September 2008 (UTC)[reply]
