Algebras of quotients with bounded evaluation of a normed semiprime algebra

M. Cabrera ¹   ; Amir A. Mohammed ²

¹ Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
² Department of Mathematics College of Education University of Mosul Mosul, Iraq

Studia Mathematica, Tome 154 (2003) no. 2, pp. 113-135

Résumé

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.

Détail

DOI : 10.4064/sm154-2-2

Keywords: algebras consisting quotients produce bounded evaluation suitable ideals multiplication algebra normed semiprime algebra these algebras quotients which contain subalgebras bounded algebras quotients have algebra seminorm which relevant inclusions continuous compute these algebras quotients norm ideals hilbert space algebras quotients bounded evaluation ideal compact operators equal banach algebra bounded linear operators algebras quotients bounded evaluation schatten p ideal infty equal schatten p ideal prove algebras quotients bounded evaluation class totally prime algebras have analytic behavior similar known bounded algebras quotients class ultraprime algebras