Abstract:
We present a generalization of the Bochner integral to locally convex spaces. This generalization preserves the nuclearity of the mapping of the space of continuous functions on a compactum represented by the Bochner integral. We introduce locally convex spaces in which the study of a broad class of vector measures with values in these spaces reduces to the study of measures with values in a normed space. The results obtained are used to describe Fréchet spaces possessing the RN property.
Citation:
V. I. Rybakov, “A generalization of the Bochner integral to locally convex spaces”, Mat. Zametki, 18:4 (1975), 577–588; Math. Notes, 18:4 (1975), 933–938
\Bibitem{Ryb75}
\by V.~I.~Rybakov
\paper A generalization of the Bochner integral to locally convex spaces
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 4
\pages 577--588
\mathnet{http://mi.mathnet.ru/mzm9972}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=399854}
\zmath{https://zbmath.org/?q=an:0325.28011}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 4
\pages 933--938
\crossref{https://doi.org/10.1007/BF01153047}
Linking options:
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This publication is cited in the following 3 articles:
E. V. Manokhin, R. A. Zhukov, I. V. Bormotov, I. V. Dobrynina, E. A. Nazyrova, “Iz istorii odnoi neopublikovannoi stati M. I. Kadetsa”, Chebyshevskii sb., 24:5 (2023), 307–319
I. V. Denisov, “Puti razvitiya matematicheskogo analiza v Tulskom gosudarstvennom pedagogicheskom universitete imeni L. N. Tolstogo (k 70-letiyu obrazovaniya kafedry matematicheskogo analiza)”, Chebyshevskii sb., 22:5 (2021), 270–306
A. I. Kirillov, “Two mathematical problems of canonical quantization. I”, Theoret. and Math. Phys., 87:1 (1991), 331–344