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For any bounded linear operator A on a (separable) Hilbert space \(\mathcal {H}\) , one wishes to describe all the (closed) subspaces \(\mathcal {M} \subseteq \mathcal {H}\) for which \(A \mathcal {M} \subseteq \mathcal {M}\) . These are called the invariant subspaces for A.Invariant subspaces For many concrete operators such as the classical Volterra operator Volterra operatoron Invariant subspacesof the shift operator \( (V f)(x) = \int _{0}^{x} f(t) dt \)

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Invariant Subspaces of the Cesàro Operator

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  • 发表日期：

    2026年

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  • Javad Mashreghi,
  • William T. Ross

摘要

For any bounded linear operator A on a (separable) Hilbert space \(\mathcal {H}\) , one wishes to describe all the (closed) subspaces \(\mathcal {M} \subseteq \mathcal {H}\) for which \(A \mathcal {M} \subseteq \mathcal {M}\) . These are called the invariant subspaces for A.Invariant subspaces For many concrete operators such as the classical Volterra operator Volterra operatoron Invariant subspacesof the shift operator \( (V f)(x) = \int _{0}^{x} f(t) dt \)