We study, from a quite general point of view, a CQ*-algebra (X, A0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative L^2 -spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, A0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative L^2-spaces.
Triolo, S. (2022). CQ -algebras of measurable operators. MOROCCAN JOURNAL OF PURE AND APPLIED ANALYSIS, 8(2), 279-285 [10.2478/mjpaa-2022-0019].
CQ -algebras of measurable operators
Triolo, S.
Primo
2022-01-01
Abstract
We study, from a quite general point of view, a CQ*-algebra (X, A0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative L^2 -spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, A0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative L^2-spaces.
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