Compact differences of composition operators

By Jennifer Moorhouse. 2005

136 citations recorded by the source corpus.

Abstract A characterization of compact difference is given for composition operators acting on the standard weighted Bergman spaces and necessary conditions are given on a larger scale of weighted Dirichlet spaces. Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts. The additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/2a169dd1dafc88f9b5077add66c83b1bdf155ba0

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Linear relations in the Calkin algebra for composition operators (2006, methodology): “The following result was established by the second author on the weighted Bergman spaces [16]; here we extend it to H(2).”
DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS (2008, background): “Differences of composition operators have been investigated more recently; see [10, 13, 14, 19] and [20].”
Compact Differences of Composition Operators on Bloch and Lipschitz Spaces (2007, background): “On the other hand, the condition of Corollary 1.2 is known to guarantee the compactness of T on various spaces, such as (weighted) Bergman and Diriclet spaces and Hardy spaces (see [ 16 ], [9]).”
Compact Differences of Composition Operators in Several Variables (2010, background): “[ [11],[12] ] Suppose φ, ψ are holomorphic self-maps of D (respectively, BN ) and suppose that there exists a sequence of points zn tending to the boundary of D (BN ) along which”
Toeplitz-Composition C*-Algebras (2006, methodology): “Now the compactness of [Cσ, T ∗ z ] follows from Theorem 3 in [19], and the compactness of Thg−h(ζ)g(ζ)Cσ is obtained as an application of Lemma 1 in [20] on compact Carleson measures of the form W (z)d(Aσ−1), with the choice W (z) = |h(z)g(z)−h(ζ)g(ζ)|2.”
Compact Differences of Composition Operators on the Bergman Spaces Over the Ball (2013, methodology): “More recently, Kriete and Moorhouse [10] extended their study to general linear combinations.”
On the connected component of compact composition operators on the Hardy space (2007, methodology): “As a main tool we use Aleksandrov–Clark measures.”