Abstract
The existence of a faithful modular representation of a left module \( \mathfrak{X} \) over a C*-algebra \( \mathfrak{A}_\# \) possessing sufficiently many traces is proved.
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Antoine, J.-P., Inoue, A., Trapani, C.: Partial *-algebras and their operator realizations. Dordrecht: Kluwer (2002)
Bagarello, F., Trapani, C.: L p-spaces as quasi *-algebras, J.Math. Anal. Appl., 197 (1996), 810–824
Bagarello, F., Trapani, C., Triolo, S.: A note on faithful traces on a von Neumann algebra, Rend. Circ. Mat. Palermo, 55 (2006), 21–28
Bagarello, F., Trapani, C., Triolo, S.: Quasi *-algebras of measurable operators, Studia Mathematica, 172 (2006), 289–305
Bagarello, F., Trapani, C.: Morphisms of certain Banach C*-modules, Publ. RIMS, Kyoto Univ., 36 (2000) 681–705
E. Nelson, Note on non-commujtative integration, J. Funct. Anal., 15 (1974) 103–116
Trapani, C., Triolo, S.: Representationsof certain BanachC*-modules, Mediterr. J.Math., 1 (2004), 441–461
Trapani, C., Triolo, S.: Representationsofmodules over a *-algebra and related seminorms, Studia Math., 184 (2008), no. 2, 133–148
Kadison, R.V., Ringrose, J.R.: Fundamentals of the Theory of Operator Algebras. Vol.II. New York: Academic Press (1986)
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Trapani, C., Triolo, S. Faithful representations of left C*-modules. Rend. Circ. Mat. Palermo 59, 295–302 (2010). https://doi.org/10.1007/s12215-010-0023-1
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DOI: https://doi.org/10.1007/s12215-010-0023-1