J. Partington

activity

20242026

collaborators

8 papers

math.FA2026

Equivalence after extension for general Toeplitz operators

M. Cristina Câmara, Jonathan R. Partington

This paper reviews the subject of equivalence after extension in the context of Toeplitz operators, truncated Toeplitz operators, and further generalizations including dual and mul…

math.FA2026

Frame constructions associated with operator orbits

Eva A. Gallardo-GutiÃ©rrez, Eva A. Gallardo-Gutiérrez, Jonathan R. Partington

This paper studies frames in Hilbert spaces generated by the orbits of (in)-finitely many vectors under a single operator, presenting new results on multiplication operators and op…

math.FA2026

Invariance and near invariance for non-cyclic shift semigroups

Yuxia Liang, Jonathan R. Partington

We characterise the subspaces of $H^{2} (D)$ that are invariant under the semigroups generated by two higher-order shifts $S^{m}$ and $S^{n}$ . Complete descriptions are obtaine…

math.FA2026

Spectra and invariant subspaces of compressed shifts on nearly invariant subspaces

Y. Liang, J. R. Partington

While the spectral properties and invariant subspaces of compressed shifts on model spaces are well understood, their behaviour on nearly $S^{*}$ -invariant subspaces, a natural gener…

math.FA2025

Composition operators between Toeplitz kernels

Yuxia Liang, Jonathan R. Partington

Recently, it was shown that the image of a Toeplitz kernel of dimension greater than $1$ under composition by an inner function is nearly $S^{*}$ -invariant if and only if the inner f…

math.FA2025

Hardy operators: In the footsteps of Brown, Halmos, and Shields

Eva A. Gallardo-Guttierrez, Jonathan R. Partington, William T. Ross

This paper discusses the two classical Hardy operators $H_{1}$ on $L^{2} (0, 1)$ and $H_{\infty}$ on $L^{2} (0, \infty)$ initially studied by Brown, Halmos and Shield…