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- An integral bilinear form is a bilinear functional that belongs to the continuous dual space of , the injective tensor product of the locally convex topological vector spaces (TVSs) X and Y. An integral linear operator is a continuous linear operator that arises in a canonical way from an integral bilinear form. These maps play an important role in the theory of nuclear spaces and nuclear maps. (en)
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- 10732 (xsd:nonNegativeInteger)
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- The dual of consists of exactly those continuous bilinear forms on that can be represented in the form of a map
:
where and are some closed, equicontinuous subsets of and , respectively, and is a positive Radon measure on the compact set with total mass
Furthermore, if is an equicontinuous subset of then the elements can be represented with fixed and running through a norm bounded subset of the space of Radon measures on (en)
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| rdfs:comment
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- An integral bilinear form is a bilinear functional that belongs to the continuous dual space of , the injective tensor product of the locally convex topological vector spaces (TVSs) X and Y. An integral linear operator is a continuous linear operator that arises in a canonical way from an integral bilinear form. These maps play an important role in the theory of nuclear spaces and nuclear maps. (en)
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- Integral linear operator (en)
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