On locally Hilbert spaces

Abstract

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. Keywords: locally Hilbert space, inductive limit, projective limit, orthocomplemented subspaces, linear functional, dual spaces. © AGH University of Science and Technology Press, 2016.