Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 397-436.

Ideals and structure of operator algebras

Authors: Melahat Almus (1), David P. Blecher (2), and Sonia Sharma (3)
Author institution: (1) Department of Mathematics, University of Houston, Houston, Texas, TX 77204-3008, U.S.A.
(2) Department of Mathematics, University of Houston, Houston, Texas, TX 77204-3008, U.S.A.
(3) Department of Mathematics, SUNY Cortland, Cortland, NY 13045, U.S.A.

Summary: We continue the study of $\mathrm r$-ideals, $\mathrm l$-ideals, and HSA's in operator algebras. Some applications are made to the structure of operator algebras, including Wedderburn type theorems for a class of operator algebras. We also consider the one-sided $M$-ideal structure of certain tensor products of operator algebras.

Keywords: Nonselfadjoint operator algebra, one-sided ideals, hereditary subalgebra, matrix units, minimal ideals, annihilator algebra, Haagerup tensor product

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