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PDF(407 KB)
PDF(407 KB)
复平面上解析Banach空间的拟不变子空间
Quasi-Invariant Subspaces in Analytic Banach Spaces over the Complex Plane
讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用，证明了Fock型空间Fp（C）={f∈Hol（C）：（1）/（π）∫C|f（z）|pe-|z|2dA（z）< +∞，1≤p< +∞}与Hilbert空间H={f∈Hol（C）：f∈Hol（C）：（1）/（π）∫C|f（z）|2e-|z|dA（z）<+∞}具有任意指标的拟不变子空间.
We investigate the existence of quasi-invariant subspaces with arbitrary index.We first give a general criterion.As applications, we show that both the Focktype spaces Fp(C)={f∈Hol(C):(1)/(π)∫C|f(z)|pe-|z|2dA(z)< +∞, 1≤p< +∞} and the Hilbert space H={f∈Hol(C):f∈Hol(C):(1)/(π)∫C|f(z)|2e-|z|dA(z)<+∞} have quasiinvariant subspaces with arbitary index.
解析Banach空间 / 拟不变子空间 / 拟不变子空间的指标 {{custom_keyword}} /
analytic Banach space / qusi-invariant subspace / index of quasi-invariant subspace {{custom_keyword}} /
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国家自然科学基金资助项目（11571248，11171245）
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