Abstract
In this chapter we shall consider the case, where \({\mathfrak A}\) is endowed with a norm topology, making \(({\mathfrak A},{{\mathfrak A}}_{\scriptscriptstyle 0})\) into a normed quasi *-algebra in the sense of Definition 3.1.1, below. This opens our discussion on locally convex quasi *-algebras, starting from the simplest situation. Nevertheless, as we shall see, simple does not mean trivial at all.
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References
J.-P. Antoine, A. Inoue, C. Trapani, Partial *-Algebras and Their Operator Realizations. Mathematics and Its Applications, vol. 553 (Kluwer, Dordrecht, 2002).
H. G. Dales, Banach Algebras and Automatic Continuity (Oxford Science Publications, Oxford, 2000)
G. Köthe, Topological Vector Spaces, vols. I and II (Springer, Berlin, 1969/1979)
T.W. Palmer, Banach Algebras and the General Theory of *-Algebras, vol. II (Cambridge University Press, Cambridge, 2001)
M. Reed, B. Simon, Methods of Modern Mathematical Physics. I. Functional Analysis (Academic Press, New York, 1972, 1980)
S. Strǎtilǎ, Modular Theory in Operator Algebras (Abacus Press, Tunbridge Wells, 1981)
S. Strǎtilǎ, L. Zsidó, Lectures on von Neumann Algebras (Editura Academiei, Bucharest and Abacus Press, Tunbridge Wells, Kent, 1979)
F. Treves, Topological Vector Spaces, Distributions and Kernels (Academic Press, New York, 1967)
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators (Wiley, New York, 1998)
M.S. Adamo, C. Trapani, Representable and continuous functionals on Banach quasi *-algebras. Mediterr. J. Math. 14, 157–181 (2017)
J.-P. Antoine, C. Trapani, F. Tschinke, Bounded elements in certain topological partial *-algebras. Stud. Math. 203, 222–251 (2011)
F. Bagarello, C. Trapani, CQ*-algebras: Structure properties. Publ. RIMS, Kyoto Univ. 32, 85–116 (1996)
F. Bagarello, C. Trapani, L p-spaces as quasi *-algebras. J. Math. Anal. Appl. 197, 810–824 (1996)
E. Nelson, Analytic vectors. Ann. Math. 70, 572–615 (1959)
I.E. Segal, A noncommutative extension of abstract integration. Ann. Math. 57, 401–457 (1953)
C. Trapani, Some seminorms on quasi *-algebras. Studia Math.. 158, 99–115 (2003); Erratum/Addendum. Stud. Math. 160, 101–101 (2004)
C. Trapani, C*-seminorms on partial *-algebras: an overview, in Proceedings of the conference on Topological Algebras and Related Topics, Bedlewo, 2003. Polish Academy of Sciences, vol. 67 (Banach Center Publications, Warsaw, 2005), pp. 369–384.
C. Trapani, Bounded elements and spectrum in Banach quasi *-algebras. Stud. Math. 172, 249–273 (2006)
C. Trapani, S. Triolo, Auxiliary seminorms and the structure of a CQ*-algebra, in Proceedings of the 5th International Conference on Functional Analysis and Approximation Theory. Rendiconti del Circolo Matematico di Palermo, vol. 76 (2005), pp. 587–601
C. Trapani, S. Triolo, Representations of modules over a ∗-algebra and related seminorms. Stud. Math. 184, 133–148 (2008)
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Fragoulopoulou, M., Trapani, C. (2020). Normed Quasi *-Algebras: Basic Theory and Examples. In: Locally Convex Quasi *-Algebras and their Representations. Lecture Notes in Mathematics, vol 2257. Springer, Cham. https://doi.org/10.1007/978-3-030-37705-2_3
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