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Spectral Properties of k-quasi-class A(s, t) Operators

Naim Latif Braha|Salah Mecheri
경북대학교 자연과학대학 수학과|2019.09|Kyungpook Mathematical Journal|제59권 제3호|pp. 415-431|DOI 10.5666/KMJ.2019.59.3.415

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키워드

Weyl's theoremw-hyponormal operatorsclass A(st)
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초록

In this paper we introduce a new class of operators which will be called the class of k-quasi-class A(s, t) operators. We show that an algebraically k-quasi-class A(s, t) operator T is polaroid, has Bishop's property and we prove that Weyl type theorems for k-quasi-class A(s, t) operators. In particular, we prove that if T is algebraically k-quasi-class A(s, t), then the generalized a-Weyl's theorem holds for T. Using these results we show that T satis es generalized the Weyl's theorem if and only if T satis es the generalized Weyl's theorem if and only if T satis es Weyl's theorem. We also examine the hyperinvariant subspace problem for k-quasi-class A(s, t) operators.

Abstract

In this paper we introduce a new class of operators which will be called the class of k-quasi-class A(s, t) operators. We show that an algebraically k-quasi-class A(s, t) operator T is polaroid, has Bishop's property and we prove that Weyl type theorems for k-quasi-class A(s, t) operators. In particular, we prove that if T is algebraically k-quasi-class A(s, t), then the generalized a-Weyl's theorem holds for T. Using these results we show that T satis es generalized the Weyl's theorem if and only if T satis es the generalized Weyl's theorem if and only if T satis es Weyl's theorem. We also examine the hyperinvariant subspace problem for k-quasi-class A(s, t) operators.

참고문헌 (41)

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