Restrictions of an invertible chaotic operator to its invariant subspaces |
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Authors: | Kit C. Chan Gokul R. Kadel |
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Affiliation: | 1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, United States;2. Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, United States |
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Abstract: | Let M be a closed subspace of a separable, infinite dimensional Hilbert space H with dim(H/M)=∞. We show that a bounded linear operator A:M→M has an invertible chaotic extension T:H→H if and only if A is bounded below. Motivated by our result, we further show that A:M→M has a chaotic Fredholm extension T:H→H if and only if A is left semi-Fredholm. |
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Keywords: | Chaotic extension Left invertibility Right invertibility Fredholm operators Invariant subspace |
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