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Covectors Are Different Than Vectors, Usually
- gus_massa 7y ago> (Fortunately, when a space of covectors is considered to be a vector space of its own, their covectors are members of the original vector space, so we never have too many vector spaces to worry about at one time.) Bad news. This is only valid in many interesting cases, but not in all cases. For example if you take * "c_0" = the space of all sequences which converge to 0, with the supreme norm * "l^1" = the space of all the sequences with and absolute sum * "l^∞" = the space of all the bounded sequences then the dual of c_0 is l^1 and the dual of l^1 is l^∞. An important general result is that the original space is included in the double dual, in this case c_0 is included in l^∞.