Affiliation:
1. Università degli Studi di Palermo
Abstract
Extensions of a positive hermitian linear functional $\omega$, defined on a dense *-subalgebra $\mathfrak{A_{0}}$ of a topological *-algebra $\mathfrak{A}[\tau]$ are analyzed. It turns out that their maximal extension as linear functionals or hermitian linear functional are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [1] is rivisited from this point of view. Examples mostly taken from the theory of integration are discussed.
Publisher
Constructive Mathematical Analysis
Subject
Applied Mathematics,Numerical Analysis,Analysis
Reference20 articles.
1. A. Bikchentaev: The algebra of thin measurable operators is directly finite, Constr. Math. Anal., 6 (1) (2023), 1–5.
2. F. Burderi, C. Trapani and S.Triolo: Extensions of hermitian linear functionals, Banach J. Math. Anal., 16 (3) (2022), 45.
3. B. Bongiorno, C. Trapani and S.Triolo: Extensions of positive linea functionals on a Topological *-algebra, Rocky Mountain Journal of Mathematics, 40 (6) (2010), 1745–1777.
4. O. Bratteli, D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics I, Springer-Verlag, Berlin (1979).
5. R. V. Kadison, J. R. Ringrose: Fundamentals of the Theory of Operator Algebras, I, Academic Press, New York (1983).