H^p上加权复合算子的刚性

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2018-09-13 DOI:10.5186/aasfm.2020.4537

M. Lindstróm, S. Miihkinen, Pekka J. Nieminen

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引用次数: 4

摘要

我们证明了作用于Hardy空间$H^p$上的每个非紧加权复合算子$f \mapsto u\cdot (f\circ\phi)$对于$1 \leq p < \infty$固定了序列空间$\ell^p$的同构副本，因此不能是严格奇异的。我们还描述了$H^p$上的那些加权复合算子，它们固定了Hilbert空间$\ell^2$的一个副本。这些结果扩展了之前对未加权复合运算符的结果。

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Rigidity of weighted composition operators on H^p

We show that every non-compact weighted composition operator $f \mapsto u\cdot (f\circ\phi)$ acting on a Hardy space $H^p$ for $1 \leq p < \infty$ fixes an isomorphic copy of the sequence space $\ell^p$ and therefore fails to be strictly singular. We also characterize those weighted composition operators on $H^p$ which fix a copy of the Hilbert space $\ell^2$. These results extend earlier ones obtained for unweighted composition operators.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.