Reducible semigroups of idempotent operators
|Title||Reducible semigroups of idempotent operators|
|Author(s)||L. Livshits, Gordon W. MacDonald, B. Mathes, H. Radjavi|
|Journal||Journal of Operator Theory|
|Abstract||We study the existence of common invariant subspaces for semigroups of idempotent operators. It is known that in finite dimensions every such semigroup is simultaneously triangularizable. The question; of the existence of even one non-trivial invariant subspace is still open in infinite dimensions. Working with semigroups of idempotent operators in Hilbert/Banach vector space settings, we exploit the connection between the purely algebraic structure and the operator structure to show that the answer is affirmative in a number of cases.|
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