바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.22 No.3

Citation Share

SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
ZUO, FEI
SHEN,, J. , & ZUO,, F. (2015). SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(3), 275-283, https://doi.org/10.7468/jksmeb.2015.22.3.275

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<sup>∗k</sup>(T<sup>∗2</sup>T<sup>2</sup> &#x2212; 2T<sup>∗</sup>T + I)T<sup>k</sup> = 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&#x2019;s theorem holds for polynomially k-quasi-2-isometric operators.

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

Reference

1.

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

2.

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

3.

Rosenblum, M.A.;. (1956). On the operator equation BX &#x2212; XA = Q. Duke Math. J., 23, 263-269. 10.1215/S0012-7094-56-02324-9.

4.

Ch&#x14D;, M.;&#xD4;ta, S.;Tanahashi, K.;Uchiyama, A.;. (2012). Spectral properties of m-isometric operators. Funct. Anal. Approx. Comput., 4(2), 33-39.

5.

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

6.

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

7.

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

8.

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.

9.

Berkani, M.;Arroud, A.;. (2004). Generalized Weyl&#x2019;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.

Ch&#x14D;, M.;&#xD4;ta, 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&#x2217;2 upper triangular operator matrices. Proc. Amer. Math. .Soc, 128, 119-123.

15.

Harte, R.E.;Lee, W.Y.;. (1997). Another note on Weyl&#x2019;s theorem. Trans. Amer. Math. Soc., 349(5), 2115-2124. 10.1090/S0002-9947-97-01881-3.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy