ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIV, 1 (2005)
p. 71 - 78

On bounded module maps between Hilbert modules over locally C*-algebras
M. Joita

Abstract.  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 $B_{b(A)}(b(E))$.

Keywords: Hilbert modules over locally C*-algebras, bounded module maps, locally m-convex algebras.

AMS Subject classification:  46L08, 46L05, 46A13.