Some authors use the term Banach space only in the case where is infinite-dimensional, although on Planetmath finite-dimensional spaces are also considered to be Banach spaces.
If is a Banach space and is any normed vector space, then the set of continuous linear maps forms a Banach space, with norm given by the operator norm. In particular, since and are complete, the continuous linear functionals on a normed vector space form a Banach space, known as the dual space of .
Finite-dimensional normed vector spaces (http://planetmath.org/EveryFiniteDimensionalNormedVectorSpaceIsABanachSpace).
spaces (http://planetmath.org/LpSpace) are by far the most common example of Banach spaces.
spaces (http://planetmath.org/Lp) are spaces for the counting measure on .
Finite (http://planetmath.org/FiniteMeasureSpace) signed measures on a -algebra (http://planetmath.org/SigmaAlgebra).
|Date of creation||2013-03-22 12:13:48|
|Last modified on||2013-03-22 12:13:48|
|Last modified by||bbukh (348)|