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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 865–870 (Mi mz1675)  

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

Diagonalization of compact operators on Hilbert modules over $C^*$-algebras of real rank zero

V. M. Manuilov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The classical Hilbert–Schmidt theorem can be extended to compact operators on Hilbert $\mathscr A$-modules over $W^*$-algebras of finite type; i.e., with minor restrictions, compact operators on $\mathscr H_\mathscr A^*$ can be diagonalized over $\mathscr A$. We show that if $B$ is a weakly dense $C^*$-subalgebra of $\mathscr A$ with real rank zero and if some additional condition holds, then the natural extension from $\mathscr H_\mathscr B$ to $\mathscr H_\mathscr A^*\supset\mathscr H_\mathscr B$ of a compact operator can be diagonalized so that the diagonal elements belong to the original $C^*$-algebra $\mathscr B$.

DOI: https://doi.org/10.4213/mzm1675

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English version:
Mathematical Notes, 1997, 62:6, 726–730

Bibliographic databases:

UDC: 517.98
Received: 31.01.1995
Revised: 29.02.1996

Citation: V. M. Manuilov, “Diagonalization of compact operators on Hilbert modules over $C^*$-algebras of real rank zero”, Mat. Zametki, 62:6 (1997), 865–870; Math. Notes, 62:6 (1997), 726–730

Citation in format AMSBIB
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\paper Diagonalization of compact operators on Hilbert modules over $C^*$-algebras of real rank zero
\jour Mat. Zametki
\yr 1997
\vol 62
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\pages 865--870
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\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 726--730
\crossref{https://doi.org/10.1007/BF02355460}
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    This publication is cited in the following articles:
    1. Keakic D.J., Lazovic Z., “Compact and “Compact” Operators on Standard Hilbert Modules Over W-Algebras”, Ann. Funct. Anal., 9:2 (2018), 258–270  crossref  mathscinet  isi  scopus  scopus
    2. Lazovic Z., “Compact and “Compact” Operators on Standard Hilbert Modules Over C-Algebras”, Adv. Oper. Theory, 3:4 (2018), 829–836  crossref  mathscinet  zmath  isi  scopus
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