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Fundam. Prikl. Mat., 1995, Volume 1, Issue 1, Pages 147–159 (Mi fpm48)  

This article is cited in 3 scientific papers (total in 3 papers)

Property of the spatial projectivity in the class of CSL-algebras with atomic commutant

Yu. O. Golovin

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

Abstract: This work continues to study spatial homological properties of, generally speaking, non-selfadjoint, reflexive operator algebras in a Hilbert space $H$. A “lattice” criterion of spatial projectivity of an algebra $A$ (i.e. the projectivity of $H$ as left Banach $A$-module) is obtained in the class of indecomposable CSL-algebras: the existence of immediate predesessor of $H$ as element of the lattice of invariant subspaces. Also, the direct product of indecomposable CSL-algebras $A_\alpha$, $\alpha\in\Lambda$, is a spatial projective algebra iff the algebra $A_\alpha$ is spatial projective for every $\alpha$.

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Received: 01.01.1995

Citation: Yu. O. Golovin, “Property of the spatial projectivity in the class of CSL-algebras with atomic commutant”, Fundam. Prikl. Mat., 1:1 (1995), 147–159

Citation in format AMSBIB
\Bibitem{Gol95}
\by Yu.~O.~Golovin
\paper Property of the spatial projectivity in the class of CSL-algebras with atomic commutant
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 1
\pages 147--159
\mathnet{http://mi.mathnet.ru/fpm48}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1789356}
\zmath{https://zbmath.org/?q=an:0877.47027}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. O. Golovin, “Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width”, Math. Notes, 63:1 (1998), 9–18  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Helemskii A.Y., “Description of spatially projective operator C*-algebras, and around it”, Banach Algebras '97, 1998, 261–272  crossref  mathscinet  zmath  isi
    3. M. E. Polyakov, “A criterion for the spatial projectivity of operator algebras possessing a canonical representation”, Russian Math. (Iz. VUZ), 45:7 (2001), 30–40  mathnet  mathscinet  zmath
  • Фундаментальная и прикладная математика
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