## $$g$$-bases in Hilbert spaces.(English)Zbl 1266.46018

Summary: The concept of $$g$$-bases in Hilbert spaces is introduced, which generalizes Schauder bases in Hilbert spaces. Some results about $$g$$-bases are proved. In particular, we characterize the $$g$$-bases and $$g$$-orthonormal bases. Dual $$g$$-bases are also discussed. We also consider the equivalent relations of $$g$$-bases and $$g$$-orthonormal bases. The property of $$g$$-minimality 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.

### MSC:

 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces

### Keywords:

$$g$$-bases; Hilbert spaces; Schauder bases
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### References:

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