학술저널
CONTINUITY OF INTERTWINING LINEAR OPERATORS WITH SHIFT OPERATORS ON Lp(R)
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 38, No. 1
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2025.0253 - 62 (10 pages)
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DOI : 10.14403/jcms.2025.38.1.53
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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.
1. Spectral subspaces of linear operators
2. Basic tools of automatic continuity
3. Intertwining linear operators with shift operators
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