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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.

Some remarks on level functions and their applications

Foralewski P., Leśnik K., Maligranda L.

Commentationes Mathematicae

2016

Vol 56, No. 1

55--86

A comparison of the level functions considered by Halperin and Sinnamon is discussed. Moreover, connections between Lorentz-type spaces, down spaces, Cesàro spaces, and Sawyer's duality formula are explained. Applying Sinnamon's ideas, we prove the duality theorem for Orlicz−Lorentz spaces which generalizes a recent result by Kamińska, Leśnik, and Raynaud (and Nakamura). Finally, some applications of the level functions to the geometry of Orlicz−Lorentz spaces are presented.