Dual Pair
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In functional analysis and related areas of mathematics a dual pair or dual system is a pair of vector spaces with an associated bilinear form. A common method in functional analysis, when studying normed vector spaces, is to analyze the relationship of the space to its continuous dual, the vector space of all possible continuous linear forms on the original space. A dual pair generalizes this concept to arbitrary vector spaces, with the duality being expressed by a b...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In functional analysis and related areas of mathematics a dual pair or dual system is a pair of vector spaces with an associated bilinear form. A common method in functional analysis, when studying normed vector spaces, is to analyze the relationship of the space to its continuous dual, the vector space of all possible continuous linear forms on the original space. A dual pair generalizes this concept to arbitrary vector spaces, with the duality being expressed by a bilinear form. Using the bilinear form, semi norms can be constructed to define a polar topology on the vector spaces and turn them into locally convex spaces, generalizations of normed vector spaces.
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