@article{3024280, title = "Locally Convex Quasi C*-Algebras and Their Structure", author = "Fragoulopoulou, M. and Trapani, C.", journal = "Lecture Notes in Mathematics", year = "2020", volume = "2257", pages = "163-200", publisher = "Springer-Verlag", doi = "10.1007/978-3-030-37705-2_7", abstract = "Throughout this chapter 0 0] denotes a unital C*-algebra and τ a locally convex topology on 0. Let 0[τ] denote the completion of 0 with respect to the topology τ. Under certain conditions on τ, a subspace of 0[τ], containing 0, will form (together with 0) a locally convex quasi *-algebra ([τ], 0), which is named locally convex quasi C*-algebra. Examples and basic properties of such algebras are presented. So, let 0[0] and τ be as before, with pλλ Λ a defining family of seminorms for τ. Suppose that τ satisfies the properties: (T1)0[ τ] is a locally convex *-algebra with separately continuous multiplication.(T2)τ 0. © 2020, Springer Nature Switzerland AG." }