Some new characterizations and g-minimality and stability of g-bases in the hilbert spaces

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. © 2013 xunxiang guo.