Copyright © 2012 Xunxiang Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.