Algebras of quotients with bounded evaluation of a normed semiprime algebra

• Autorzy: M. Cabrera , Amir A. Mohammed
• Języki publikacji: EN

Abstrakty

EN

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 ≤ p<∞) 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.

Kategorie tematyczne

• 46H10: Ideals and subalgebras
• 16S90: Torsion theories; radicals on module categories
• 46H20: Structure, classification of topological algebras
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 154
• Numer: 2
• Strony: 113-135

Daty

wydano

2003

Twórcy

autor

M. Cabrera

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

Amir A. Mohammed

• Department of Mathematics, College of Education, University of Mosul, Mosul, Iraq

Identyfikatory

DOI

10.4064/sm154-2-2