CONTINUITY OF INTERTWINING LINEAR OPERATORS WITH SHIFT OPERATORS ON Lp(R)

• 발행기관: 충청수학회
• 저자명: Hyuk Han
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 38, No. 1, 53~62쪽, 전체 10쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2025.02.28

국문 초록

In this paper, we show that for an isometry T acting on a Banach space X, the analytic spectral subspace XT (F) coincides with the algebraic spectral subspace ET (F) for any closed subset F of C. Using this, we have the following result. For p, q ∈ [1,∞) and a linear operator θ : Lp(R) → Lq(R), if Taθ = θTa for some a ∈ R \ {0}, then θ is automatically continuous, where Ta is the shift operator.

목차

1. Spectral subspaces of linear operators

2. Basic tools of automatic continuity

3. Intertwining linear operators with shift operators

References

키워드

automatic continuity local spectral theory intertwining operator