Algebras of quotients with bounded evaluation of a normed semiprime algebra
Volume 154 / 2003
Abstract
We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra $A$. These algebras of quotients, which contain $A$, are subalgebras of the bounded algebras of quotients of $A$, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space $H$: 1) the algebras of quotients with bounded evaluation of the ideal of all compact operators on $H$ are equal to the Banach algebra of all bounded linear operators on $H$, 2) the algebras of quotients with bounded evaluation of the Schatten $p$-ideal on $H$ (for $1\le p<\infty $) are equal to the Schatten $p$-ideal on $H$. We also prove that the algebras of quotients with bounded evaluation on the class of totally prime algebras have an analytic behavior similar to the one known for the bounded algebras of quotients on the class of ultraprime algebras.
