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arXiv · 1902.07689

Kernel maps and operator decomposition

Gabriel Matos·Lina Oliveira
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Abstract

We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that every norm closed Lie module of a continuous nest algebra is decomposable. The continuity of the nest cannot be lifted, in general.

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Gabriel Matos, Lina Oliveira. 2019-02-20. Kernel maps and operator decomposition. https://doi.org/10.1007/s43037-019-00012-6

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