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Journal of Function Spaces
Volume 2016 (2016), Article ID 9516839, 8 pages
http://dx.doi.org/10.1155/2016/9516839
Research Article

On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, Azerbaijan
2Baku State University, Azerbaijan

Received 17 November 2015; Accepted 11 February 2016

Academic Editor: Miguel Martín

Copyright © 2016 Migdad Ismailov et al. 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 -frame which is a generalization of the frame in Hilbert spaces generated by the bilinear mapping is considered. -frame operator is defined; analogues of some well-known results of frame theory are obtained in Hilbert spaces. Conditions for the existence of -frame in Hilbert spaces are obtained; the relationship between the definite bounded surjective operator and -frame is also studied. The concept of -orthonormal -basis is introduced.