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Bounded elements and spectrum in Banach quasi<sup>*</sup>-algebras
A normal Banach quasi $^*$-algebra $({\mathfrak X},)$ has a distinguished Banach $^*$-algebra ${\mathfrak X}_{\rm b}$ consisting of {bounded} elements of ${\mathfrak X}$. The latter $^*$-algebra is shown to coincide with the set of elements of ${\mathfrak