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An operator T ∈ L(H), is said to belong to k-quasi class A∗n operator if T∗k(|Tn+1|2/n+1 - |T∗|2)Tk≥O for some positive integer n and some positive integer k.
First, we will see some properties of this class of operators and prove Weyl’s theorem for algebraically k-quasi class A ∗ n . Second, we consider the tensor product for k-quasi class A ∗ n , giving a necessary and sufficient condition for T ⊗ S to be a k-quasi class A ∗ n , when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class A ∗ n operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and (B ∗ ) −1 are k-quasi class A ∗ n operators such that AX = XB, then A ∗ X = XB ∗ . Finally, we will prove the spectrum continuity of this class of operators.
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참고문헌 (33)
참고문헌 신청
A. Aluthge / 1990 / On p-hyponormal operators for 0 < p < 1 / Integral Equations Operator Theory 13 (3) : 307 ~ 315
A. Brown / 1966 / Spectra of tensor products of operators / Proc. Amer. Math. Soc 17 : 162 ~ 166
B. Fuglede / 1950 / A Commutativity theorem for normal operator / Proc. Natl. Acad. Sci. USA 36 : 35 ~ 40
B. P. Duggal / 2010 / Continuity of the spectrum on a class of upper triangular operator matrices / J. Math. Anal. Appl 370 (2) : 584 ~ 587
B. P. Duggal / 2012 / On *-paranormal contractions and properties for *-class A operators / Linear Algebra Appl 436 (5) : 954 ~ 962
A. Brown / 1966 / Spectra of tensor products of operators / Proc. Amer. Math. Soc 17 : 162 ~ 166
B. Fuglede / 1950 / A Commutativity theorem for normal operator / Proc. Natl. Acad. Sci. USA 36 : 35 ~ 40
B. P. Duggal / 2010 / Continuity of the spectrum on a class of upper triangular operator matrices / J. Math. Anal. Appl 370 (2) : 584 ~ 587
B. P. Duggal / 2012 / On *-paranormal contractions and properties for *-class A operators / Linear Algebra Appl 436 (5) : 954 ~ 962
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