Abstract and Applied Analysis

g -Bases in Hilbert Spaces

Xunxiang Guo

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 923729, 14 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475991

Digital Object Identifier
doi:10.1155/2012/923729

Mathematical Reviews number (MathSciNet)
MR3004882

Zentralblatt MATH identifier
1266.46018

Citation

Guo, Xunxiang. $g$ -Bases in Hilbert Spaces. Abstr. Appl. Anal. 2012 (2012), Article ID 923729, 14 pages. doi:10.1155/2012/923729. https://projecteuclid.org/euclid.aaa/1364475991


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