대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제16권1호
  • /
  • Pages.25-66
  • /
  • 2001
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

작용소의 틈이론

  • 정일봉 (경북대학교 자연과학대학 수학과) ;
  • 이우영 (성균관대학교 자연과학부 수학과)
  • 발행 : 2001.01.01
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⟨ 이전 논문 다음 논문 ⟩

초록

복소힐버트 공간상에서 정의된 작용소 중에서 최근 많이 연구되는 분야는 부분정규작용소와 초정규작용소들 들 수 있다. 본 논문에서는 작용소의 부분정규성과 초정규성 사이에 있는 작용소의 여러 성질을 살펴보고 특히 $\textsc{k}$차초정규, 이차약초정규, 삼차약초정규, 다항초정규, 토에플리츠작용소 및 약부분정규작용소에 관한 최근의 연구 결과들을 살펴보며 이와 관련되 미해결 문제들을 제시한다. 마지막으로 틈이론의 응용으로서 작용소이론의 큰 문제인 불변공간문제와의 관련성을 살펴보고 틈이론의 전망과 기타 관련정보를 소개한다.

키워드

참고문헌

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