Research PaperNo Access

-Controlled frames in Hilbert $C^{}$ $C^{*}$ -modules

Tayebe Lal Shateri

Tayebe Lal Shateri

Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, P. O. Box 397, Iran

E-mail Address: t.shateri@hsu.ac.ir

E-mail Address: shateri@ualberta.ca

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https://doi.org/10.1142/S0219691320500800Cited by:0 (Source: Crossref)

Abstract

The main purpose of this paper is to introduce the notion of *-T-controlled frames in Hilbert $C^{*}$ $C^{*}$ -modules. We present some results of frames in the view of *-T-controlled frames in Hilbert $C^{*}$ $C^{*}$ -modules. Also, we define *-w-frames and give their relations to *-T-controlled frames and multiplier operators.

Keywords:

AMSC: Primary 42C15, Secondary 06D22

References

1. L. Arambaic , On frames for countably generated Hilbert $C^{*}$ $C^{*}$ -modules, Proc. Amer. Math. Soc. 135 (2007) 479–478. Web of Science, Google Scholar
2. P. Balazs, J.-P. Antoine and A. Grybos , Weighted and controlled frames, Int. J. Wavelets, Multiresolut. Inf. Process. 8(1) (2010) 109–132. Link, Web of Science, Google Scholar
3. P. G. Casazza and G. Kutyniok , Frames of subspaces, in Wavelets, Frames and operator theory, Contemp. Math. 345 (2004) 87–113. Crossref, Google Scholar
4. O. Christensen , An Introduction to Frames and Riesz Bases (Birkhäuser, Boston, 2016). Google Scholar
5. I. Daubechies, A. Grassman and Y. Meyer , Painless nonorthogonal expansions, J. Math. Phys. 27 (1986) 1271–1283. Crossref, Web of Science, Google Scholar
6. R. J. Duffin and A. C. Schaeffer , A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952) 341–366. Crossref, Web of Science, Google Scholar
7. M. Frank and D. R. Larson , Frames in Hilbert $C^{*}$ $C^{*}$ -modules and $C^{*}$ $C^{*}$ -algebras, J. Operator Theory 48 (2002) 273–314. Web of Science, Google Scholar
8. W. Jing, Frames in Hilbert $C^{*}$ $C^{*}$ -modules, Ph.D. thesis, University of Central Florida Orlando, Florida (2006). Google Scholar
9. A. Khosravi and B. Khosravi , g-frames and modular Riesz bases in Hilbert $C^{*}$ $C^{*}$ -modules, Int. J. Wavelets Multiresolut. Inf. Process. 10(2) (2012) 1–12. Link, Web of Science, Google Scholar
10. A. Nejati and A. Rahimi , Generalized frames in Hilbert spaces, Bull. Iranian Math. Soc. 35(1) (2009) 97–109. Web of Science, Google Scholar
11. M. Rashidi-Kouchi and A. Rahimi , On controlled frames in Hilbert $C^{*}$ $C^{*}$ -modules, Int. J. Wavelets Multiresolut. Inf. Process. 15(4) (2017) 1750038, https://doi.org/10.1142/S0219691317500382. Link, Web of Science, Google Scholar
12. W. Sun , G-frames and g-Riesz bases, J. Math. Anal. Appl. 322(1) (2006) 437–452. Crossref, Web of Science, Google Scholar
13. X. Xiao, Y. Zhu and L. Gavruta , Some properties of K-frames in Hilbert spaces, Results Math. 63(3–4) (2013) 1243–1255. Crossref, Web of Science, Google Scholar