Invariant Subspaces for Semigroups of Algebraic Operators |
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| Authors: | Grega Cigler Roman Drnovšek Damjana Kokol-Bukovšek Matja? Omladi? Thomas J Laffey Heydar Radjavi Peter Rosenthal |
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| Institution: | aFaculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia;bDepartment of Mathematics, University College of Dublin, Dublin, 4, Ireland;cDepartment of Mathematics, Delhousie University, Halifax, Nova Scotia, Canada, B3H 3J5;dDepartment of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 1A1 |
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| Abstract: | T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable. |
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