Search
Search Results
-
Operators with a non-trivial closed invariant affine subspace
We are concerned with the question of the existence of an invariant proper affine subspace for an operator A on a complex Banach space. It turns out...
-
Cowen–Douglas Operators and Shift Operators
In this paper, we attempt to understand Cowen–Douglas operators by the way of basis theory and shift operator. For a Cowen–Douglas operator
... -
Kernels of perturbed Toeplitz operators in vector-valued Hardy spaces
Recently, Liang and Partington (Integr Equ Oper Theory 92(4): 35, 2020) show that kernels of finite-rank perturbations of Toeplitz operators are...
-
Compressions of
k th-order slant Toeplitz operators to model spacesIn this paper, we consider compressions of k th-order slant Toeplitz operators to the backward shift-invariant subspaces of the classical Hardy space H
-
Paired Kernels and Their Applications
This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space
... -
Multivariable Beurling–Lax representations: the commutative and free noncommutative settings
The original theorem of Beurling asserts that any invariant subspace for the shift operator (multiplication by the coordinate function
... -
Complementing Nonuniqueness Sets in Model Spaces
It is shown that any incomplete system of reproducing kernels in a model subspace K θ = H 2 ⊖ θH 2 of the Hardy space H 2 can be complemented to a...
-
Recent Developments in the Interplay Between Function Theory and Operator Theory for Block Toeplitz, Hankel, and Model Operators
This is a semi-expository paper on some recent developments in the interplay between function theory and operator theory in the context of Toeplitz,...
-
Inner Outer Factorization of Wide Rational Matrix Valued Functions on the Half Plane
The main purpose of this note is to use operator methods to solve a rational inner-outer factorization problem for wide functions. It is believed...
-
Compact Operators and Kernel Bundles
As a bridge between matrices (or finite rank operators) and linear operators on an infinite dimensional Hilbert space...
-
Some Basic Properties of Hypercyclic Operators
Using a few classical examples and the invariant subspace problem, we motivate the definition of a hypercyclic operator on a Banach space. We state a...
-
Hilbert Spaces
This chapter introduces the notion of a complex Hilbert space, which is an infinite-dimensional complex vector space with an inner product. Hilbert...
-
On growth and instability for semilinear evolution equations: an abstract approach
We propose a new approach to the study of (nonlinear) growth and instability for semilinear abstract evolution equations with compact nonlinearities....
-
Decomposability, past and present
We discuss the concept of decomposability for operators from its inception to present applications.
-
The work of Pavlov on shift operators on a Riemann surface
Boris Pavlov’s mathematical quest was centered on the interplay between operator theory, complex analysis, and mathematical physics. More...
-
Dilation theory and analytic model theory for doubly commuting sequences of C·0-contractions
It is known that every C ·0 -contraction has a dilation to a Hardy shift. This leads to an elegant analytic functional model for C ·0 -contractions, and...