Unitary dilations of multi-parameter semigroups of operators
Erratum to the paper "On the reflexivity of pairs of isometries and of tensor products of some reflexive algebras" (Studia Math. 83 (1986), 47-55)
A gap in the proof of [4, Theorem 1] is removed.
The algebra generated by a pair of operator weighted shifts
We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.
On the reflexivity of pairs of isometries and of tensor products of some operator algebras
Unitary dilation and fixed point theorem
Continuous isometric semigroups and reflexivity
Abstract. We consider the reflexivity of a WOT-closed algebra generated by continuous isometric semigroups parametrized by the semigroup of non-negative reals or the semigroup of finite sequences of non-negative reals. It is also proved that semigroups of continuous unilateral multi-parameter shifts are reflexive.
On the reflexivity and hyperreflexivity of algebras and subspaces
A review of recent reflexivity and hyperreflexivity results is presented. We concentrate particularly on a finite-dimensional situation, Toeplitz operators and partial isometries. Open problems in this area are given.
Projections onto the spaces of Toeplitz operators
Projections onto the spaces of all Toeplitz operators on the N-torus and the unit sphere are constructed. The constructions are also extended to generalized Toeplitz operators and applied to show hyperreflexivity results.
Reflexivity of Toeplitz operators in multiply connected regions
Subspaces of Toeplitz operators on the Hardy spaces over a multiply connected region in the complex plane are investigated. A universal covering map of such a region and the group of automorphisms invariant with respect to the covering map connect the Hardy space on this multiply connected region with a certain subspace of the classical Hardy space on the disc. We also present some connections of Toeplitz operators on both spaces from the reflexivity point of view.
Quasinormal operators are hyperreflexive
We will prove the statement in the title. We also give a better estimate for the hyperreflexivity constant for an analytic Toeplitz operator.
On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane
The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between spaces on the unit circle and the real line...
On the reflexivity of multigenerator algebras
CONTENTS1. Introduction...................................................................................................52. N-tuples of linear transformations in finite-dimensional space......................83. Toeplitz operators on the polydisc and the unit ball....................................184. Subspaces of weighted shifts.....................................................................235. Joint spectra for N-tuples of operators........................................................276....
Properties of two variables Toeplitz type operators
The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.
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