Existence of spectral well-behaved \(\ast\)-representations
Given an unbounded \(m^{*}\)-seminorm \(p\) of a \(*\)-algebra, a \(p\)-spectral \(*\)-representation is studied in connection with well-behaved \(*\)-representations. The existence of well-behaved \(p\)-spectral \(*\)-representations on \(*\)-algebras is characterized through certain properties of Ptak functions on the domain of \(p\). Also, the existence of a spectral well-behaved \(*\)-representation of a locally convex \(*\)-algebra is studied in terms of the properties of Ptak functions defined on the \(*\)-subalgebra generated by selfajoint elements of the set of Allan bounded elements. Finally, the authors examine the existence of \(p\)-spectral well-behaved \(*\)-representations in several classes of locally convex \(*\)-algebras.
spectral and \(p\)-spectral \(\ast\)-representation
scientific article; zbMATH DE number 5017395
scientific article