Geodesic
On bounded module maps between Hilbert modules over locally C * -algebras
Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 1 
M. Joita. On bounded module maps
between Hilbert modules over locally C * -algebras. Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2005_74_1_a6/
@article{AMUC_2005_74_1_a6,
     author = {M. Joita},
     title = {On bounded module maps
between {Hilbert} modules over locally {C} * -algebras},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2005},
     volume = {74},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2005_74_1_a6/}
}
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between Hilbert modules over locally C * -algebras
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Voir la notice de l'article provenant de la source Comenius University

Let $A$ be a locally $C^{*}$-algebra and let $E$ be a Hilbert $A$-module. We show that the algebra $B_A(E)$ of all bounded $A$-module maps on $E$ is a locally \hbox{$m$-c}on\-vex algebra which is algebraically and topologically isomorphic to $LM(K_A(E))$, the algebra of all left multipliers of $K_A(E)$, where $K_A(E)$ is the locally $C^{*}$-algebra of all ''compact`` $A$-module maps on $E$. Also we show that $b(B_A(E))$, the algebra of all bounded elements in $B_A(E)$, is a Banach algebra which is isometrically isomorphic to $B_{b(A)}(b(E))$.