Algebras of quotients with bounded evaluation of a normed semiprime algebra

M. Cabrera, and Amir A. Mohammed. "Algebras of quotients with bounded evaluation of a normed semiprime algebra." Studia Mathematica 154.2 (2003): 113-135. <http://eudml.org/doc/284441>.

@article{M2003,
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 ≤ 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.},
author = {M. Cabrera, Amir A. Mohammed},
journal = {Studia Mathematica},
keywords = {normed semiprime algebra; totally prime algebra},
language = {eng},
number = {2},
pages = {113-135},
title = {Algebras of quotients with bounded evaluation of a normed semiprime algebra},
url = {http://eudml.org/doc/284441},
volume = {154},
year = {2003},
}

TY - JOUR
AU - M. Cabrera
AU - Amir A. Mohammed
TI - Algebras of quotients with bounded evaluation of a normed semiprime algebra
JO - Studia Mathematica
PY - 2003
VL - 154
IS - 2
SP - 113
EP - 135
AB - 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.
LA - eng
KW - normed semiprime algebra; totally prime algebra
UR - http://eudml.org/doc/284441
ER -