Continuous Linear Functionals
See also: Continuous linear operatorIf V is a topological vector space, the space of continuous linear functionals — the continuous dual — is often simply called the dual space. If V is a Banach space, then so is its (continuous) dual. To distinguish the ordinary dual space from the continuous dual space, the former is sometimes called the algebraic dual. In finite dimensions, every linear functional is continuous, so the continuous dual is the same as the algebraic dual, although this is not true in infinite dimensions.
Read more about this topic: Linear Functional
Famous quotes containing the word continuous:
“For Lawrence, existence was one continuous convalescence; it was as though he were newly reborn from a mortal illness every day of his life. What these convalescent eyes saw, his most casual speech would reveal.”
—Aldous Huxley (1894–1963)