International Journal of Mathematics Trends and Technology
Volume 46 | Number 2 | Year 2017 | Article Id. IJMTT-V46P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P516
In this paper, we recall basic definitions of topological algebras, normed algebras, Banach algebras, involutive algebras, and C*-algebras. We also give many elementary examples for these algebras. Different types of frame operators is explained. Norms on frame operator is defined. Some results on eigen values and eigen vectors is proved.
1. j. Cahill and P. G. Casazza, The Paulsen Problem in operator theory, Preprint (2012).
2. J. Cahill, P. G. Casazza, and S. Li, Pliicker embeddings and optimal generic frames, In Preparation.
3. P. G. Casazza, M. Fickus, J. C. Tremain, and E. Weber, The Kadison-Singer Problem in mathematics and engineering- A detailed account, Contemp. Math. 414, “Operator theory, operator algebras and applications”, D. Han, P. E. T. Jorgensen, and D. R. Larson, eds., (2006),297-356.
4. K. Grocheing, Foundations of Time-Frequency Analysis, Birkhauser, Boston, MA (2001).
5. J. Kovacevic and A. Chebira, Life beyond bases: The advent of frames (part 1), IEEE Single Proc. Mag. 24 (2007), 86-104.
6. R.J. Duffin and A. C. Schaeffer, A class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc 72 (1952), 2, 341-366.
7. J. Dixmier, C∗-algebras. North-Holland publishing company, Inc. Amesterdam, New York, Oxford, (1977).
8. N. Dunford, J. T. Schwartz, Lieanr operators, Part I: general theory. John Wiley and Sons, Inc. (1957).
Kalyani Pendyala, "Lecture Notes on Frame Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 2, pp. 95-100, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P516
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