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Mat. Sb., 1992, Volume 183, Number 11, Pages 75–98 (Mi msb1090)  

On the theory of infinite-dimensional superspace: reflexive Banach supermodules

A. Yu. Khrennikov


Abstract: A study is made of reflexive Banach supermodules of sequences of elements of a supercommutative Banach superalgebra. The theory of Hilbert supermodules, introduced as isomorphic to the supermodule $l_2(\Lambda)$, is of greatest interest for applications. An analogue of the Riesz theorem on representation of a continuous $\Lambda$-linear functional is proved for Hilbert supermodules.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:2, 331–350

Bibliographic databases:

UDC: 517.948
MSC: Primary 58C50, 58A50; Secondary 46H25, 16W55, 17A70
Received: 31.10.1991

Citation: A. Yu. Khrennikov, “On the theory of infinite-dimensional superspace: reflexive Banach supermodules”, Mat. Sb., 183:11 (1992), 75–98; Russian Acad. Sci. Sb. Math., 77:2 (1994), 331–350

Citation in format AMSBIB
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\paper On the theory of infinite-dimensional superspace: reflexive Banach supermodules
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\yr 1992
\vol 183
\issue 11
\pages 75--98
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..331K}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 2
\pages 331--350
\crossref{https://doi.org/10.1070/SM1994v077n02ABEH003444}
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