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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.
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참고문헌 (15)
참고문헌 신청
B.P. Duggal / 2010 / Continuity of the spectrum on a class of upper triangular operator matrices / J. Math. Anal. Appl 370 : 584 ~ 587
B.P. Duggal / 2012 / On -paranormal contractions and prop-erties for - class A operators / Linear Algebra Appl 436 : 954 ~ 962
D. Xia / 1983 / Spectral Theory of Hyponormal Operators / Birkhauser Verlag
D.R. Farenick / 1996 / Hyponormality and spectra of Toeplitz operators / Trans. Amer. Math. Soc 348 : 4153 ~ 4174
I.S. Hwang / 1998 / On the continuity of spectra of Toeplitz operators / Arch. Math 70 : 66 ~ 73
B.P. Duggal / 2012 / On -paranormal contractions and prop-erties for - class A operators / Linear Algebra Appl 436 : 954 ~ 962
D. Xia / 1983 / Spectral Theory of Hyponormal Operators / Birkhauser Verlag
D.R. Farenick / 1996 / Hyponormality and spectra of Toeplitz operators / Trans. Amer. Math. Soc 348 : 4153 ~ 4174
I.S. Hwang / 1998 / On the continuity of spectra of Toeplitz operators / Arch. Math 70 : 66 ~ 73
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