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Mat. Zametki, 1976, Volume 20, Issue 4, Pages 511–520 (Mi mz7871)  

This article is cited in 1 scientific paper (total in 1 paper)

Some stability properties for analytic operator functions

Yu. L. Shmul'yan

Odessa Institute of Marine Engineers

Abstract: Let $\mathfrak G$ be a connected, finite-dimensional, complex analytic manifold; let T(lambda) be an analytic function defined on $\mathfrak G$, whose values are $J$-biexpanding operators on a $J$-space $H$. Let $\mathfrak R(A)$ denote the range of $A$. The following assertions are proved: 1. The lineals $\mathfrak R(\sqrt{T(\lambda)^*JT(\lambda)-J})\equiv\mathfrak R$ and $\mathfrak R(\sqrt{T(\lambda)JT(\lambda)^*-J})\equiv\mathfrak R_*$ do not depend on $\lambda$. 2. For arbitrary $\lambda,\mu\in\mathfrak G$ we have $\mathfrak R(T(\lambda)-T(\mu))\subset\mathfrak R_*$, $\mathfrak R(T(\lambda)^*-T(\mu)^*)\subset\mathfrak R$.

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English version:
Mathematical Notes, 1976, 20:4, 843–848

Bibliographic databases:

Received: 19.07.1974

Citation: Yu. L. Shmul'yan, “Some stability properties for analytic operator functions”, Mat. Zametki, 20:4 (1976), 511–520; Math. Notes, 20:4 (1976), 843–848

Citation in format AMSBIB
\Bibitem{Shm76}
\by Yu.~L.~Shmul'yan
\paper Some stability properties for analytic operator functions
\jour Mat. Zametki
\yr 1976
\vol 20
\issue 4
\pages 511--520
\mathnet{http://mi.mathnet.ru/mz7871}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=428085}
\zmath{https://zbmath.org/?q=an:0346.47017}
\transl
\jour Math. Notes
\yr 1976
\vol 20
\issue 4
\pages 843--848
\crossref{https://doi.org/10.1007/BF01098900}


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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. M. Arlinskii, “Closed sectorial forms and one-parameter contraction semigroups”, Math. Notes, 61:5 (1997), 537–546  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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