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Eurasian Mathematical Journal, 2015, Volume 6, Number 4, Pages 44–58
(Mi emj209)
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This article is cited in 5 scientific papers (total in 5 papers)
Invertibility of multivalued sublinear operators
I. V. Orlovab, S. I. Smirnovaa a Department of Mathematics and Informatics, Crimean Federal V. Vernadsky University, 4 Academician Vernadsky Avenue, Simferopol, Republic Crimea, Russia, 295007
b Voronezh State University, 1 University Square, Voronezh, Russia, 394006
Abstract:
We consider the representation of a compact-valued sublinear operator ($K$-operator) by means of the compact convex packet of single-valued so-called basis selectors. Such representation makes it possible to introduce the concept of an invertible $K$-operator via invertible selectors. The extremal points of direct and inverse selector representations are described, an analogue of the von Neumann theorem is obtained. A series of examples is considered.
Keywords and phrases:
sublinear multivalued operators, basis selectors, Hamel basis, extremal points.
Received: 11.10.2015
Citation:
I. V. Orlov, S. I. Smirnova, “Invertibility of multivalued sublinear operators”, Eurasian Math. J., 6:4 (2015), 44–58
Linking options:
https://www.mathnet.ru/eng/emj209 https://www.mathnet.ru/eng/emj/v6/i4/p44
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Abstract page: | 421 | Full-text PDF : | 99 | References: | 38 |
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