[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b170025

ON m-ISOMETRIC TOEPLITZ OPERATORS

Ko, Eungil (Department of Mathematics Ewha Womans University)
Lee, Jongrak (Institute of Mathematical Sciences Ewha Womans University)

Publication Information

Bulletin of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 367-378 More about this Journal

Abstract

In this paper, we study m-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize m-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols ${\varphi}$ . In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols ${\varphi}$ to be m-expansive or m-contractive. Finally, we give some results for m-expansive and m-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols ${\varphi}$ .

Keywords

m-isometric operators; expansive operators; contractive operators; Toeplitz operators;

Citations & Related Records

Reference

1	L. J. Patton and M. E. Robbins, Composition operators that are m-isometries, Houston J. Math. 31 (2005), no. 1, 255-266.
2	P. Y. Wu, Hyponormal operators quasisimilar to an isometry, Trans. Amer. Math. Soc. 291 (1985), no. 1, 229-239. DOI
3	T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Amer. Math. Soc. 338 (1993), no. 2, 753-767. DOI
4	F. Botelho, On the existence of n-isometries on ${\ell}_{p}$ spaces, Acta Sci. Math. (Szeged) 76 (2010), no. 1-2, 183-192.
5	J. Agler, A disconjugacy theorem for Toeplitz operators, Amer. J. Math. 112 (1990), no. 1, 1-14. DOI
6	J. Agler and M. Stankus, m-isometric transformations of Hilbert space. I, Integral Equations Operator Theory 21 (1995), no. 4, 383-429. DOI
7	J. Agler and M. Stankus, m-isometric transformations of Hilbert space. III, Integral Equations Operator Theory 24 (1996), no. 4, 379-421. DOI
8	O. A. M. Sid Ahmed, m-isometric operators on Banach spaces, Asian-Eur. J. Math. 3 (2010), no. 1, 1-19. DOI
9	T. Bermudez, A. Martinon, and J. A. Noda, Products of m-isometries, Linear Algebra Appl. 438 (2013), no. 1, 80-86. DOI
10	A. Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/1964), 89-102.
11	M. Cho, T. Nakazi, and T. Yamazaki, Hyponormal operators and two-isometry, Far East J. Math. Sci. (FJMS) 49 (2011), no. 1, 111-119.
12	C. C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), no. 3, 809-812. DOI
13	J. Agler and M. Stankus, m-isometric transformations of Hilbert space. II, Integral Equations Operator Theory 23 (1995), no. 1, 1-48. DOI
14	I. S. Hwang and W. Y. Lee, Hyponormal Toeplitz operators with rational symbols, J. Operator Theory 56 (2006), no. 1, 47-58.
15	D. Farenick, M. Mastnak, and A. I. Popov, Isometries of the Toeplitz matrix algebra, J. Math. Anal. Appl. 434 (2016), no. 2, 1612-1632. DOI
16	M. F. Gamal, On Toeplitz operators similar to isometries, J. Operator Theory 59 (2008), no. 1, 3-28.
17	T. A. Grigoryan, E. V. Lipacheva, and V. H. Tepoyan, On the extension of the Toeplitz algebra by isometries, in The varied landscape of operator theory, 137-146, Theta Ser. Adv. Math., 17, Theta, Bucharest.
18	C. A. McCarthy, $c_{p}$ , Israel J. Math. 5 (1967), 249-271. DOI