A Note on Hyperinvariance

Abstract

본 논문에서는 무한복소 Hilbert 공간에서 한 유계선형변환의 불변부분공간들이 초불변부분공간이 될 충분조건과 세가지 유형의 초불변부분공간을 소개하였다.

In this paper, several sufficient conditions for hyperinvariance and three hyperinvariant subspaces are introduced.

If A is reductive operator, then A can be written as a direct sum A₁?? A₂ where A₁ is normal, A₂ is reductive and all the invariant subspaces of A₂ are hypervariant.

More generally, if A be an operator, there exist two types of hyperinvariant subspaces ??(F) and S??(b).

In this paper, several sufficient conditions for hyperinvariance and three hyperinvariant subspaces are introduced.

If A is reductive operator, then A can be written as a direct sum A₁?? A₂ where A₁ is normal, A₂ is reductive and all the invariant subspaces of A₂ are hypervariant.

More generally, if A be an operator, there exist two types of hyperinvariant subspaces ??(F) and S??(b).