Abstract
In this (and the next) section the main statements of infinite-dimensional distributions theory are stated; this material seems to have a considerable independent interest. Up to the end of the section Z is a Hilbert space, H is a linearly and densely enclosed in Z Hilbert space and the imbedding operator I: H → Z is absolutely summing (= is a Hilbert—Shmidt operator). We denote by T a natural isomorphism of Z on Z* (so that for ∀ z 1, z 2 ∈ Z the equalities \({\left( {{z_1},{z_2}} \right)_Z} = {\left( {T{z_1},{z_2}} \right)_H}\mathop {{\text{ }} = }\limits^{def} \left( {T{z_1},{z_2}} \right) = {\left( {T{z_1},{z_2}} \right)_{Z*}}\) hold. T is conjugate with I with respect to the scalar compositions in Z and H).
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© 2000 Springer Science+Business Media Dordrecht
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Uglanov, A.V. (2000). Applications. In: Integration on Infinite-Dimensional Surfaces and Its Applications. Mathematics and Its Applications, vol 496. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9622-0_5
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DOI: https://doi.org/10.1007/978-94-015-9622-0_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5384-8
Online ISBN: 978-94-015-9622-0
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