Multipliers and cyclic vectors in the Bloch space.

@article{Brown1991MultipliersAC,
  title={Multipliers and cyclic vectors in the Bloch space.},
  author={Leon Brown and Allen L. Shields},
  journal={Michigan Mathematical Journal},
  year={1991},
  volume={38},
  pages={141-146}
}
Multiplicative Isometries and Isometric Zero-Divisors
Abstract For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular
Mean Ergodicity of Multiplication Operators on the Bloch and Besov Spaces
In this paper, the power boundedness and mean ergodicity of multiplication operators are investigated on the Bloch space $\mathcal{B}$, the little Bloch space $\mathcal{B }_0 $ and the Besov Space
Weighted composition operators on the Bloch space
  • S. Ohno, R. Zhao
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2001
We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and
Holomorphic semigroups and Sarason’s characterization of vanishing mean oscillation
It is a classical theorem of Sarason that an analytic function of bounded mean oscillation (BMOA), is of vanishing mean oscillation if and only if its rotations converge in norm to the original
Closure in the Logarithmic Bloch Norm of Dirichlet Type Spaces
TLDR
This paper characterize the closure of Dirichlet type space with respect to logarithmic Bloch space, and revisits a description of the boundedness of composition operator.
Invertible and isometric weighted composition operators
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted
On model spaces and density of functions regular on the boundary
We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It turns out that such approximation is possible if and only if the singular measure associated to
On model spaces and density of functions smooth on the boundary
We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to
Products of Unbounded Bloch Functions
  • D. Girela
  • Mathematics
    Operator Theory, Functional Analysis and Applications
  • 2021
We give new constructions of pair of functions (f, g), analytic in the unit disc, with g ∈ H∞ and f an unbounded Bloch function, such that the product g ⋅ f is not a Bloch function.
MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE
Let M(X,Y ) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlettype spaces D α, M(D p−1,D q q−1) = {0}, if p 6= q, 0 < p, q < ∞. If 0 <
...
...