Measure, Integration & Real Analysis · Problem 10A.13

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · left-right-invertible-open-sets

Problem

Suppose VV is a Hilbert space. (a) Show that {T∈B(V):T is left invertible}\{T \in \mathcal{B}(V) : T \text{ is left invertible}\} is an open subset of B(V)\mathcal{B}(V). (b) Show that {T∈B(V):T is right invertible}\{T \in \mathcal{B}(V) : T \text{ is right invertible}\} is an open subset of B(V)\mathcal{B}(V).

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