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Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach. (Russian, English) Zbl 1112.46005
Zap. Nauchn. Semin. POMI 331, 60-83 (2006); translation in J. Math. Sci., New York 141, No. 4, 1417-1428 (2007).
Authors’ abstract: In the framework of idempotent mathematics, some analogs for the well-known kernel theorems of L. Schwartz and A. Grothendieck are examined. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are described. An algebraic approach is used, so topological concepts and results are simulated by means of algebraic tools.
Reviewer: Josef Wloka (Kiel)

MSC:
46A99 Topological linear spaces and related structures
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
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