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On the bounded part of a Hilbert module over a locally C *-algebra

Periodica Mathematica Hungarica
Volume/Issue:
Volume 45: Issue 1-2
DOI:
https://doi.org/10.1023/a:1022350030495
Author: Maria Joiţa

Abstract  

We will show that the bounded part of the locally C*-algebra of all adjointable operators on the Hilbert A-module E is isomorphic to the C*-algebra Lb(A)(b(E)) of all adjointable operators on the Hilbert b(A)-module b(E).

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On Hilbert modules over locally C*-algebras II

Periodica Mathematica Hungarica
Volume/Issue:
Volume 51: Issue 1
DOI:
https://doi.org/10.1007/s10998-005-0018-4
Author: Maria Joiţa

Summary  

In this paper we study the unitary equivalence between Hilbert modules over a locally \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $C^{*}$ \end{document}-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $C^{*}$ \end{document}-algebra and show that a Hilbert module over a Fr\'{e}chet locally \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $C^{*}$ \end{document}-algebra is countably generated if and only if the locally \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $C^{*}$ \end{document}-algebra of all ``compact'' operators has an approximate unit.

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