Journal of Operator Theory

Volume 54, Issue 1, Summer 2005 pp. 69-92.

Continuous Versions of the Littlewood-Richardson Rule, Selfadjoint Operators, and Invariant Subspaces

Authors: Hari Bercovici (1) and Wing Suet Li (2) and Thomas Smotzer (3)
Author institution: (1) Mathematics Department, Indiana University, Bloomington, IN 47405, USA, (2) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA, (3) Mathematics Department, Youngstown State University, Youngstown, OH 44555, USA

Summary: We establish the equivalence of two continuous versions of the Littlewood-Richardson rule. We also show how these rules give alternate characterizations for the eigenvalues of a sum of compact selfadjoint operators. Finally, applications to the invariant subspaces of nilpotent one parameter operator semigroups are given.

Keywords: Horn inequalities, Littlewood-Richardson rule, invariant subspaces, selfadjoint operator.

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