Opuscula Math. 36, no. 6 (2016), 735-747

Opuscula Mathematica

On locally Hilbert spaces

Aurelian Gheondea

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.

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  • Aurelian Gheondea
  • Bilkent University, Department of Mathematics, 06800 Bilkent, Ankara, Turkey
  • Institutul de Matematică al Academiei Române, C.P. 1-764, 014700 Bucureşti, România
  • Communicated by P.A. Cojuhari.
  • Received: 2016-04-02.
  • Accepted: 2016-09-14.
  • Published online: 2016-10-29.
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Cite this article as:
Aurelian Gheondea, On locally Hilbert spaces, Opuscula Math. 36, no. 6 (2016), 735-747, http://dx.doi.org/10.7494/OpMath.2016.36.6.735

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