Linear Functional - Continuous Linear Functionals

Continuous Linear Functionals

See also: Continuous linear operator

If 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:

    I can never get people to understand that poetry is the expression of excited passion, and that there is no such thing as a life of passion any more than a continuous earthquake, or an eternal fever. Besides, who would ever shave themselves in such a state?
    George Gordon Noel Byron (1788–1824)