Opuscula Math. 36, no. 6 (2016), 735-747
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.
Mathematics Subject Classification: 46A13, 46C05, 46E99.