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The spectral theorem for locally normal operators

Gheondea A.

Opuscula Mathematica

2018

Vol. 38, no. 5

597--662

We prove the spectral theorem for locally normal operators in terms of a locally spectral measure. In order to do this, we first obtain some characterisations of local projections and we single out and investigate the concept of a locally spectral measure.

On locally Hilbert spaces

Gheondea A.

Opuscula Mathematica

2016

Vol. 36, no. 6

735--747

This is an investigation of some basic properties of strictly inductive limits of Hilbert spaces, called locally Hilbert spaces, with respect to their topological properties, the geometry of their subspaces, linear functionals and dual spaces.