Search results
Results from the WOW.Com Content Network
In mathematics, specifically in order theory and functional analysis, the order dual of an ordered vector space is the set where denotes the set of all positive linear functionals on , where a linear function on is called positive if for all , implies () [1] The order dual of is denoted by +.
Consequently, the dual space is an important concept in functional analysis. Early terms for dual include polarer Raum [Hahn 1927], espace conjugué, adjoint space [Alaoglu 1940], and transponierter Raum [Schauder 1930] and [Banach 1932]. The term dual is due to Bourbaki 1938. [1]
In functional analysis, the dual norm is a measure of size for a continuous linear function defined on a normed vector space. ... this dual space is also a Hilbert ...
The space of distributions, being defined as the continuous dual space of (), is then endowed with the (non-metrizable) strong dual topology induced by () and the canonical LF-topology (this topology is a generalization of the usual operator norm induced topology that is placed on the continuous dual spaces of normed spaces).
The Erdős–Kaplansky theorem is a theorem from functional analysis.The theorem makes a fundamental statement about the dimension of the dual spaces of infinite-dimensional vector spaces; in particular, it shows that the algebraic dual space is not isomorphic to the vector space itself.
In mathematics, a dual system, dual pair or a duality over a field is a triple (,,) consisting of two vector spaces, and , over and a non-degenerate bilinear map:.. In mathematics, duality is the study of dual systems and is important in functional analysis.
The dual ′ of a normed vector space is the space of all continuous linear maps from to the base field (the complexes or the reals) — such linear maps are called "functionals".
Functional analysis is a branch of mathematical analysis, ... contrary to the finite-dimensional situation. This is explained in the dual space article.