941 research outputs found
Operator equations and invariant subspaces
No full textBanach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A2=B2 and if A has nontrivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.</p
Composition operators and a pull-back measure formula
No full textA pull-back measure formula obtained in some particular cases by E. A. Nordgren and this author is generalized in the framework of boundary measures for zero-free Nevanlinna class fuctions on the unit polydisk. The formula is used to characterize the zero-free Nevanlinna class functions which are solutions of Schröder\u27s equation induced by a polydisk automorphism ϕ (i.e. to determine the zero-free functionsf belonging to the Nevanlinna class which are solutions of the functional equationf ° π=λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author
Numerical ranges of composition operators
No full textAbstractComposition 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 symbol fixes 0 and has infinity norm less than 1 have closed numerical ranges in the shape of a cone-like figure, i.e., a closed convex region with a corner at 1, 0 in its interior, and no other corners. Compact composition operators induced by a univalent symbol whose fixed point is not 0 have numerical ranges without corners, except possibly a corner at 0
Alf Nilsen-Børsskog — The Author Chosen by the Language
No full textThis article discusses Alf Nilsen-Børsskog’s four-volume series of novels Elämän jatko [Continuation of life, 2004–2015], seen as the first literary works treating the Kven culture from a native perspective. Nilsen-Børsskog’s novels are analysed as constituting a “counterstory”, a term coined in the postcolonial cultural research paradigm to refer to self-representation. The Kvens have been considered a national minority in Norway since 1999, and their language has been an official minority language since 2005. The present author scrutinizes how Nilsen-Børsskog’s work differs from previous literary descriptions of this minority, often marked by the frequent use of stereotypes of the Kven language and culture
A fixed point theorem for analytic functions
No full text We prove that each analytic self-map of the open unit disk which interpolates between certain -tuples must have a fixed point.</p
The eigenfunctions of a certain composition operator
No full textAbstract. The composition operator on the classical Hardy space H2, induced by a hyperbolic disk automorphism is considered. It is investigated when a H2-function induces under the given operator a minimal invariant cyclic subspace. Theorems where we use the behaviour of this function in the neighbourhood of the fixed points of the hyperbolic automorphism in order to decide if the cyclic subspace mentioned above is minimal invariant or not, are obtained. The inner eigenfunctions of the operator under consideration are characterized. 1
On spectra of composition operators
No full textIn 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 of a composition operator (valid in select cases), in terms of the aforementioned Nikodym derivative, is established. Estimates of the spectra of adjoints of composition operators are obtained. Based on them, we describe the spectrum of composition operators induced by maps fixing a point, whose iterates exhibit a strong form of attractiveness to that point
COMPOSITION OPERATORS WHOSE SYMBOLS HAVE ORTHOGONAL POWERS
No full textComposition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal pow-ers 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 consid-eration is a non–inner map with a fixed point in the unit disk. The canonical decomposition of a non–unitary composition contraction is determined
Invertible and normal composition operators on the Hilbert Hardy space of a half–plane
No full textOperators 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
Composition operators similar to contractions
No full textOperators of type f→f◦φ acting on function spaces are called composition operators. We consider composition operators acting on the Hilbert Hardy space on the open unit disc or the right half-plane, study when they are similar to contractions, and obtain results interesting from the point of view of dilation theory of contractions and function theory
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