6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Lina Oliveira

Invariant subspace lattices and kernel maps

We introduce the concept of the kernel map of an operator relative to a subspace lattice, outlining some of its properties and applications. In particular, we use these maps to show that any finite rank operator in a norm closed Lie module of a continuous nest algebra can be decomposed as a sum of finitely many rank-1 operators in the module. The hypothesis of the continuity of the nest cannot be dropped, in general.

The talk is based on joint work with Gabriel Matos.

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