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Some properties of heminormal and perinormal operators

Title
Some properties of heminormal and perinormal operators
Authors
윤지선
Issue Date
2009
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
김경화
Abstract
이 논문에서는 heminormal과 perinormal 작용소에 대해서 공부한다. 특히, binormal 작용소상에서는 k-hyponormal, hyponormal, semihyponormal 그리고 qusihyponormal 작용소가 동치임을 증명한다. 또한, heminormal 작용소의 거듭제곱과 양의 제곱근은 heminormal이 아님을 보인다. 마지막으로 perinormal의 몇 가지 성질을 공부한다.;In this thesis, we study heminormal and perinormal operators. In partic-ular, we show that if T ∈ L(H) is a binormal operator, then the following statements are equivalent; (1) an operator T is k-hyponormal for some positive integer k, (2) an operator T is hyponormal, (3) an operator T is semihyponormal, and (4) an operator T is quasihyponormal. Also, we show that some power and square root of a heminormal operator are not necessarily heminormal. Finally, we study some properties of perinormal operators.
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일반대학원 > 수학과 > Theses_Master
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