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Mat. Zametki, 1998, Volume 63, Issue 1, Pages 9–20 (Mi mz1243)  

This article is cited in 2 scientific papers (total in 2 papers)

Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width

Yu. O. Golovin

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: This paper is concerned with the connection between the geometric properties of the lattice $L$ of subspaces of a Hilbert space $H$ and homological properties (flatness and injectivity) of $H$ regarded as a natural module over the reflexive algebra $\operatorname{Alg}L$ that consists of all operators leaving invariant each element of the lattice $L$. It follows from these results that the cohomology groups with coefficients in $\mathscr B(H)$ are trivial for a broad class of reflexive algebras.

DOI: https://doi.org/10.4213/mzm1243

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English version:
Mathematical Notes, 1998, 63:1, 9–18

Bibliographic databases:

UDC: 512.745.2
Received: 28.06.1996

Citation: Yu. O. Golovin, “Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width”, Mat. Zametki, 63:1 (1998), 9–20; Math. Notes, 63:1 (1998), 9–18

Citation in format AMSBIB
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\by Yu.~O.~Golovin
\paper Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width
\jour Mat. Zametki
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\pages 9--20
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\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 1
\pages 9--18
\crossref{https://doi.org/10.1007/BF02316138}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Polyakov, ME, “An example of a spatially non-flat von Neumann algebra”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 4:1 (2001), 1  crossref  mathscinet  zmath  isi  scopus  scopus
    2. O. Yu. Aristov, “On approximation of flat Banach modules by free modules”, Sb. Math., 196:11 (2005), 1553–1583  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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