Bijectivity of *-Endomorphisms of ...(H) and the Unilateral Shift.
Bounded elements and spectrum in Banach quasi *-algebras
A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra consisting of bounded elements of . The latter *-algebra is shown to coincide with the set of elements of having finite spectral radius. If the family () of bounded invariant positive sesquilinear forms on contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of ().