g-Bases in Hilbert Spaces

الملخص EN

The concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces.

Some results about g-bases are proved.

In particular, we characterize the g-bases and g-orthonormal bases.

And the dual g-bases are also discussed.

We also consider the equivalent relations of g-bases and g-orthonormal bases.

And the property of g-minimal of g-bases is studied as well.

Our results show that, in some cases, g-bases share many useful properties of Schauder bases in Hilbert spaces.