SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2015, v.22 no.3, pp.275-283

https://doi.org/10.7468/jksmeb.2015.22.3.275

SHEN, JUNKI (COLLEGE OF COMPUTER AND INFORMATION TECHNOLOGY, HENAN NORMAL UNIVERSITY)
ZUO, FEI (HENAN ENGINEERING LABORATORY FOR BIG DATA STATISTICAL, ANALYSIS AND OPTIMAL CONTROL, SCHOOL OF MATHEMATICS AND INFORMATION SCIENCE, HENAN NORMAL UNIVERSITY)

SHEN, JUNKI, & ZUO, FEI. (2015). SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS. 한국수학교육학회지시리즈B:순수및응용수학, 22(3), 275-283, https://doi.org/10.7468/jksmeb.2015.22.3.275

복사

Abstract

Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T∗k(T∗2T2 − 2T∗T + I)Tk = 0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl’s theorem holds for polynomially k-quasi-2-isometric operators.

keywords: k-quasi-2-isometric operator, polaroid, generalized Weyl’s theorem.

참고문헌

Laursen, K.B.;Neumann, M.M.;. Introduction to Local Spectral Theory.

Patel, S.M.;. (2002). 2-isometry operators. Glasnik Mat., 37(57), 143-147.

Rosenblum, M.A.;. (1956). On the operator equation BX − XA = Q. Duke Math. J., 23, 263-269. 10.1215/S0012-7094-56-02324-9.

Chō, M.;Ôta, S.;Tanahashi, K.;Uchiyama, A.;. (2012). Spectral properties of m-isometric operators. Funct. Anal. Approx. Comput., 4(2), 33-39.

Duggal, B.P.;. (2012). Tensor product of n-isometries. Linear Algebra Appl., 437, 307-318. 10.1016/j.laa.2012.02.017.

Agler, J.;. (1990). A disconjugacy theorem for Toeplitz operators. Amer. J. Math., 112(1), 1-14. 10.2307/2374849.

Agler, J.;Stankus, M.;. (1995). m-isometric transformations of Hilbert space. I. Integral Equ. Oper. Theory, 21(4), 383-429. 10.1007/BF01222016.

Bermudez, T.;Martinon, A.;Negrin, E.;. (2010). Weighted shift operators which are m-isometry. Integral Equ. Oper. Theory, 68, 301-312. 10.1007/s00020-010-1801-z.

Berkani, M.;Arroud, A.;. (2004). Generalized Weyl’s theorem and hyponormal operators. J. Austra. Math. Soc., 76(2), 291-302. 10.1017/S144678870000896X.

10.

Berkani, M.;Koliha, J.J.;. (2003). Weyl type theorems for bounded linear operators. Acta Sci. Math.(Szeged), 69(1-2), 359-376.

11.

Berkani, M.;Sarih, M.;. (2001). On semi B-Fredholm operators. Glasgow Math. J., 43(3), 457-465.

12.

Chō, M.;Ôta, S.;Tanahashi, K.;. (2013). Invertible weighted shift operators which are m-isometries. Proc. Amer. Math. Soc., 141(12), 4241-4247. 10.1090/S0002-9939-2013-11701-6.

13.

Duggal, B.P.;. (2007). Polaroid operators, SVEP and perturbed Browder, Weyl theorems. Rendiconti Circ Mat di Palermo LVI, 56, 317-330. 10.1007/BF03032085.

14.

Han, J.K.;Lee, H.Y.;. (1999). Invertible completions of 2∗2 upper triangular operator matrices. Proc. Amer. Math. .Soc, 128, 119-123.

15.

Harte, R.E.;Lee, W.Y.;. (1997). Another note on Weyl’s theorem. Trans. Amer. Math. Soc., 349(5), 2115-2124. 10.1090/S0002-9947-97-01881-3.

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논문 상세

Vol.22 No.3

SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS

SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학