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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
A Remark On The Multipliers On Spaces Of Weak Products Of Functions, Stefan Richter, Brett D. Wick
A Remark On The Multipliers On Spaces Of Weak Products Of Functions, Stefan Richter, Brett D. Wick
Mathematics Faculty Publications
Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
Invertible And Normal Composition Operators On The Hilbert Hardy Space Of A Half–Plane, Valentin Matache
Invertible And Normal Composition Operators On The Hilbert Hardy Space Of A Half–Plane, Valentin Matache
Mathematics Faculty Publications
Operators on function spaces of form... is a fixed map are called composition operators with symbol φ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
On Spectra Of Composition Operators, Valentin Matache
On Spectra Of Composition Operators, Valentin Matache
Mathematics Faculty Publications
In this paper we consider composition operators Cφ on the Hilbert Hardy space over the unit disc, induced by analytic selfmaps φ. We use the fact that the operator C∗φCφ is asymptotically Toeplitz to obtain information on the essential spectrum and spectrum of Cϕ, which we are able to describe in select cases (including the case of some hypercyclic composition operators or that of composition operators with the property that the asymptotic symbol of C∗φCφ is constant a.e.). One of our tools is the Nikodym derivative of the pull-back measure induced by φ. An alternative formula for the essential norm …
Numerical Ranges Of Composition Operators With Inner Symbols, Valentin Matache
Numerical Ranges Of Composition Operators With Inner Symbols, Valentin Matache
Mathematics Faculty Publications
Operators on function paces acting by composition to the right with a fixed self-map φ of some set are called composition operators with the symbol φ. In this paper, composition operators on the Hilbert Hardy space over the unit disk are considered. The numerical ranges of composition operators with inner symbol of parabolic automorphic type of hyperbolic type are shown to be circular.
Composition Operators Whose Symbols Have Orthogonal Powers, Valentin Matache
Composition Operators Whose Symbols Have Orthogonal Powers, Valentin Matache
Mathematics Faculty Publications
Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non–inner map with a fixed point in the unit disk. The canonical decomposition of a non–unitary composition contraction is determined.
Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond
Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond
Mathematics Faculty Publications
We prove that any composition operator with maximal norm on one of the weighted Bergman spaces is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space H2, where every inner function induces a composition operator with maximal norm.
Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer
Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer
Mathematics Faculty Publications
We establish a condition that guarantees isolation in the space of composition operators acting between H p (B N ) and H q (B N ), for 0 < p ≤ ∞, 0 < q < ∞, and N ≥ 1. This result will allow us, in certain cases where 0 < q < p ≤ ∞, completely to characterize the component structure of this space of operators.
Numerical Ranges Of Composition Operators, Valentin Matache
Numerical Ranges Of Composition Operators, Valentin Matache
Mathematics Faculty Publications
Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 is a fixed point of the symbol. If 0 is not a fixed point of the symbol 1 is shown to be interior to the numerical range. Some composition operators whose …