Some New Characterizations and g-Minimality and Stability of g-Bases in the Hilbert Spaces

الملخص EN

The concept of g-basis in the Hilbert spaces is introduced by Guo (2012) who generalizes the Schauder basis in the Hilbert spaces.

g-basis plays the similar role in g-frame theory to that the Schauder basis plays in frame theory.

In this paper, we establish some important properties of g-bases in the Hilbert spaces.

In particular, we obtain a simple condition under which some important properties established in Guo (2012) are still true.

With these conditions, we also establish some new interesting properties of g-bases which are related to g-minimality.

Finally, we obtain a perturbation result about g-bases.