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Some properties of 2-expansive operators

Title
Some properties of 2-expansive operators
Authors
정주연
Issue Date
2012
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
고응일
Abstract
본 논문에서는 2-expansive 작용소를 공부한다. 먼저 unilateral weighted shift가 2-expansive 작용소가 되는 필요충분조건을 구한다. 이 결과로부터 2-expansivity에 관한 여러 가지 예제들을 제공한다. 또한 2-expansive 작용소의 모든 거듭제곱이 2-expansive가 됨을 보인다. 더 나아가 2-expansive 작용소의 스펙트럼에 관한 성질들을 제공한다. 특히, 작용소 T가 2-expansive이면 T가 유니터리이거나 스펙트럼이 닫힌 단위 원판이 됨을 증명한다. 따름정리로써 모든 2-expansive 작용소가 isoloid임을 보인다.;In this thesis, we study 2-expansive operators. We first obtain an equivalent condition for unilateral weighted shifts to be 2-expansive. From this consequence, we provide several examples concerning 2-expansivity. We also show that every power of a 2-expansive operator is again 2-expansive. Furthermore, we give some spectral properties of 2-expansive operators. In particular, we verify that if T∈L(H) is 2-expansive, then either T is unitary or σ(T) = cl(D), where D denotes the open unit disk in C. As a corollary, we get that every 2-expansive operator is isoloid.
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