Can someone dumb it down a little what is a dual space of the Banach space V?
Dual spaces Watch
- Thread Starter
- 09-12-2010 02:25
- 09-12-2010 12:37
It's (usually defined as) the vector space of all continuous (a.k.a. bounded) linear functionals on V. So if I say , then f is a function (or if you are working with a complex Banach space) which is continuous (or bounded, under the operator norm) and linear.
Very rarely, the dual space is defined generically as the space of all linear functionals on V - including the discontinuous / unbounded ones. This is valid for any vector space V, whereas the above definition requires a normed vector space.