Components of linear-fractional composition operators☆

By Paul S. Bourdon. 2003

61 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c66fb5007cafd870f2c157c92ab99c12f9234bc2

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Compact Differences of Composition Operators in Several Variables (2010, background): “impliﬁed proof of this result in one variable. The fact that a diﬀerence of linear-fractional composition operators cannot be non-trivially compact on H2(D) or A2 α(D) was ﬁrst obtained by P. Bourdon [2] and J. Moorhouse [12] as a consequence of results on the compactness of a diﬀerence of more gene”
On compactness of the difference of composition operators (2004, methodology): “Then define the discs Dk,j = B (1 dk,j)ei/k,dk,je 20·2”
Which linear-fractional composition operators are essentially normal?☆ (2003, background): “In [ 2 ] it is shown that if extra smoothness assumptions are placed on ! and ,, then boundary data agreement up to second order derivatives is necessary for compactness of C! %C).”
On the connected component of compact composition operators on the Hardy space (2007, background): “Does any non-compact composition operator belong to CompK(H (2))? The general form (A) of the Shapiro–Sundberg conjecture has recently been answered negatively by Moorhouse and Toews [18] and Bourdon [4].”
Toeplitz-Composition C*-Algebras (2006, background): “Since a difference of non-compact linear-fractional composition operators is compact only if it is zero ([2], [18]), the result follows.”
Linear relations in the Calkin algebra for composition operators (2006, background): “The final Section 6 concerns a problem first studied by Berkson [2], subsequently considered by MacCluer [13], Shapiro and Sundberg [26], and most recently by Toews and the second author [17] and Bourdon [3]: to characterize those pairs φ and ψ for which Cφ and Cψ lie in the same connected component”