Reducible semigroups of idempotent operators

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Title Reducible semigroups of idempotent operators
Author(s) L. Livshits, Gordon W. MacDonald, B. Mathes, H. Radjavi
Journal Journal of Operator Theory
Date 1998
Volume 40
Issue 1
Start page 35
End page 69
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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