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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 2 | Year 2019 | Article Id. IJMTT-V65I2P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I2P506

Product of Composition Operators


Dr. S. K. Latha
Abstract

In this paper it is proved that the product of two composition operators  C1 and C2 with  h2 h1 = 1 and h1 =  h1 o T2 is quasi isometry and 2-isometry. Also it I s proved that this condition is not necessary for C1 and  C2 with an example.

Keywords
Isometric operators, Composition Operators
References

[1] Agler. J and Stankus. M, m-isometries transformations of Hilbert space, I. Integral Equations and Operator theory, 21(1995), 383-427.
[2] S. Panayappan, Non–Hyponormal Composition Operators, Indian Journal of Math. 35(1993), 293-98.
[3] Patel S. M., 2- Isometric Operators, Glasnik Matematicki, Vol 37 (57) (2002) 143-147.
[4] Patel S. M., A note on Quasi-isometries, Glasnik Matematicki, Vol 35 (55) (2000) 307-312.
[5] Pushpa, R. Suri and Singh.N., M-quasihyponormal Composition operators, Inter. J. Math and Math. Sci., 10(3) , (1987), 621-623.
[6] Singh. R. K., Compact and quasinormal composition operators, Proc. Amer. Math. Soc. 45 (1974), 80-82.
[7] Singh R.K. and David Chandrakumar, R, Some results on Composition operators, Indian Journ. Pure Appl. Math., 14(10) (1983), 1233-1237.
[8] K. Thirugnanasambandam, Class Q composition operators on L2 spaces, Thesis, May 2009, Bharathiar University, India.
[9] S. Panayappan, Non-normal Composition operators on L2 spaces, Thesis, 1993-Bharathiar University, India.
[10] S. Panayappan, S. K. Latha, Some Isometric Composition Operators, Int. J. Contemp. math. Sciences, Vol.5, 2010, no 13, 615-621.

Citation :

Dr. S. K. Latha, "Product of Composition Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 2, pp. 27-30, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I2P506

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