Structural and spectral properties of $k$-quasi-$*$-paranormal operators
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
For a positive integer $k$, an operator $T$ is said to be $k$-quasi-$*$-paranormal if $||T^{k+2}x||||T^{k}x||\geq||T^{*}T^{k}x||^{2}$ for all $x\in H$, which is a generalization of $*$-paranormal operator. In this paper, we give a necessary and sufficient condition for $T$ to be a $k$-quasi-$*$-paranormal operator. We also prove that the spectrum is continuous on the class of all $k$-quasi-$*$-paranormal operators.
Abstract
For a positive integer $k$, an operator $T$ is said to be $k$-quasi-$*$-paranormal if $||T^{k+2}x||||T^{k}x||\geq||T^{*}T^{k}x||^{2}$ for all $x\in H$, which is a generalization of $*$-paranormal operator. In this paper, we give a necessary and sufficient condition for $T$ to be a $k$-quasi-$*$-paranormal operator. We also prove that the spectrum is continuous on the class of all $k$-quasi-$*$-paranormal operators.
참고문헌 (15)
- S.K. Berberian, "Approximate proper vectors", Proc. Amer. Math. Soc, 13, pp.111~114 (1962)
- J.B. Conway, "Operators that are points of spectral continuity", Integr. Equ. Oper. Theory, 2, pp.174~198 (1979)
- S.V. Djordjevic, "Continuity of the essential spectrum in the class of quasihy-ponormal operators", Vesnik Math, 50, pp.71~74 (1998)
- B.P. Duggal, "Continuity of the spectrum on a class of upper triangular operator matrices", J. Math. Anal. Appl, 370, pp.584~587 (2010)
- B.P. Duggal, "On -paranormal contractions and prop-erties for - class A operators", Linear Algebra Appl, 436, pp.954~962 (2012)
- D.R. Farenick, "Hyponormality and spectra of Toeplitz operators", Trans. Amer. Math. Soc, 348, pp.4153~4174 (1996)
- P.R. Halmos, "A Hilbert Space Problem Book" (1982), Springer-Verlag
- J.K. Han, "Invertible completions of 2 2 upper triangular operator matrices", Proc. Amer. Math. Soc, 128, pp.119~123 (1999)
- Y.M. Han, "A note on -paranormal operators", Integr. Equ. Oper. Theory, 49(4), pp.435~444 (2004)
- S. Mecheri, "On a new class of operators and Weyl type theorems", Filomat, 27, pp.629~636 (2013)
- S. Mecheri, "On quasi--paranormal operators", Ann. Funct. Anal, 3(1), pp.86~91 (2012)
- I.S. Hwang, "On the continuity of spectra of Toeplitz operators", Arch. Math, 70, pp.66~73 (1998)
- I.S. Hwang, "The spectrum is continuous on the set of p-hyponormal operators", Math. Z, 235, pp.151~157 (2000)
- J.L. Shen, "The spectrum properties of quasi--paranormal oper-ators", Chinese Annals of Math, 34(6), pp.663~670 (2013)
- D. Xia, "Spectral Theory of Hyponormal Operators" (1983), Birkhauser Verlag