WEYL’S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS A ∗ n OPERATORS

• Published in: Journal of the Korean Mathematical Society pp. 1089 - 1104
• Main Authors: Ilmi Hoxha, Naim Latif Braha
• Format: Journal Article
• Language: English
• Published: 대한수학회 01.09.2014
• Subjects: 수학
• ISSN: 0304-9914; 2234-3008
• DOI: 10.4134/JKMS.2014.51.5.1089

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. KCI Citation Count: 0