Revision as of 19:38, 12 July 2013 edit 83.104.224.106 (talk) tiny typo correction ← Previous edit		Revision as of 20:14, 31 December 2013 edit undo I3roly (talk \| contribs) 52 edits I think that what was trying to be said is the complex space of \ell^2 is richer than that of the reals (example seems to follow same structure) Next edit →
Line 19: Complex-valued [[Lp space\|L<sup>2</sup> spaces]] on [[measure (mathematics)\|sets with a measure]] have a particular importance because they are [[Hilbert space]]s. They often appear in [[functional analysis]] (for example, in relation with [[Fourier transform]]) and [[operator theory]]. A major user of such spaces is [[quantum mechanics]], as [[wave function]]s. AThe sets on ~~that~~which the complex-valued L<sup>2</sup> is constructed ~~may~~have the potential to be ~~rather~~more exotic than their real-valued analog. For example, complex-valued [[function space]]s are used in some branches of [[p-adic analysis\|{{mvar\|p}}-adic analysis]] for algebraic reasons: complex numbers form an [[algebraically closed field]] (which facilitates operator theory), whereas neither real numbers nor {{mvar\|p}}-adic numbers are not. Also, complex-valued [[continuous function]]s are an important example in the theory of [[C*-algebra]]s: see [[Gelfand representation]].

Complex-valued function: Difference between revisions