Restrictions of an Invertible Chaotic Operator to Its Invariant Subspaces
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.
Chan, Kit C. and Kadel, Gokul R., "Restrictions of an Invertible Chaotic Operator to Its Invariant Subspaces" (2014). Mathematics and Statistics Faculty Publications. 33.
Journal of Mathematical Analysis and Applications
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