Stable and Norm-stable Invariant Subspaces

Alexander Borichev; Don Hadwin; Hassan Yousefi

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arXiv · 1001.1018

Stable and Norm-stable Invariant Subspaces

Alexander Borichev·Don Hadwin·Hassan Yousefi

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Abstract

We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are the finite-dimensional ones. We also characterize norm-stable invariant subspaces of any weighted unilateral shift operator. We show that quasianalytic shift operators are points of norm continuity of the lattice of the invariant subspaces. We also provide a necessary condition for strongly stable invariant subspaces for certain operators.

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BibTeX RIS

Alexander Borichev, Don Hadwin, Hassan Yousefi. 2010-08-18. Stable and Norm-stable Invariant Subspaces. https://arxiv.org/abs/1001.1018

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