Zobrazeno 1 - 10
of 341
pro vyhledávání: '"Partington, Jonathan R."'
We give a complete characterisation of the linear isometries of ${\rm Hol}(\Omega)$, where $\Omega$ is the half-plane, the complex plane or an annulus centered at 0 and symmetric to the unit circle. Moreover, we introduce new techniques to describe t
Externí odkaz:
http://arxiv.org/abs/2409.16105
This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are generalizations of
Externí odkaz:
http://arxiv.org/abs/2409.02563
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and also, somewh
Externí odkaz:
http://arxiv.org/abs/2408.14120
Autor:
Liang, Yuxia, Partington, Jonathan R.
This paper characterises the subspaces of $H^2(\mathbb D)$ simultaneously invariant under $S^2 $ and $S^{2k+1}$, where $S$ is the unilateral shift, then further identifies the subspaces that are nearly invariant under both $(S^2)^*$ and $(S^{2k+1})^*
Externí odkaz:
http://arxiv.org/abs/2408.08659
Rhaly operators, as generalizations of the Ces\`aro operator, are studied from the standpoint of view of spectral theory and invariant subspaces, extending previous results by Rhaly and Leibowitz to a framework where generalized Ces\`aro operators ar
Externí odkaz:
http://arxiv.org/abs/2408.03182
Autor:
Liang, Yuxia, Partington, Jonathan R.
Recently, we proved that the image of a Toeplitz kernel of dimension $>1$ under composition by an inner function is nearly $S^*$-invariant if and only if the inner function is an automorphism. In this paper, we build on this work and describe the min
Externí odkaz:
http://arxiv.org/abs/2405.19875
Autor:
Liang, Yuxia, Partington, Jonathan R.
In this paper, the structure of the nearly invariant subspaces for discrete semigroups generated by several (even infinitely many) automorphisms of the unit disc is described. As part of this work, the near $S^*$-invariance property of the image spac
Externí odkaz:
http://arxiv.org/abs/2309.08306
This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are generalizations of Toepl
Externí odkaz:
http://arxiv.org/abs/2308.16644
This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of the first t
Externí odkaz:
http://arxiv.org/abs/2307.06923
This paper is concerned with paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space. By considering when such operators commute, generalizations of the Brown--Halmos results for Toeplitz ope
Externí odkaz:
http://arxiv.org/abs/2304.07252