Topological structure of the space of composition operators onH∞

By Barbara Maccler, Shuichi Ohno, R. Zhao. 2001

125 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/080713485638b2e00fbd5815b8d14c1381668720

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In Algebra and Number Theory

In Applied Mathematics

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Citations in the corpus

Compact Differences of Composition Operators on Bloch and Lipschitz Spaces (2007, methodology): “Let us recall here that the answer is positive in the larger space H∞ of bounded analytic functions [11].”
DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS (2008, background): “H1 ! H1, see [ 19 ] Example 1. The change of the behaviour of the operator C` iCˆ depending on the weights v and w is emphasized in our last example.”
Compact differences of composition operators (2005, methodology): “[15] used the pseudo-hyperbolic metric to give equivalent conditions for compactness of composition operators acting on H∞.”
On the connected component of compact composition operators on the Hardy space (2007, background): “Also, in the setting of H, the space of bounded analytic functions, a complete description of the component structure of Comp(H) was found in [14].”
Topological Structure of the Space of Weighted Composition Operators on H∞ (2005, methodology): “Thus we get Cϕ ≈ Cψ. On the other hand, by Theorem 1o f [ 9 ],Cϕ and Cψ are not in the same connected component of C(H ∞ ).”
Isolated points and essential components of composition operators on H^c^h^i (2001, background): “Theorem 3 in [8] is restated as follows.”
DIFFERENCES OF COMPOSITION OPERATORS ON THE BLOCH SPACES (2007, background): “By [6], it is shown that dρ(φ, ψ) < 1 and there is a curve γ from φ to ψ in the topological space S(D, dρ).”
On compactness of the difference of composition operators (2004, methodology): “Observe that [ MOZ ] established the equivalence of conditions (3) and (5) of the following result.”
Weighted Composition Operators between Different Hardy Spaces (2003, background): “Since about 1980, this subject has undergone explosive growth (see, for example, the following recent papers [ 21 ], [25]).”
Essential norm of the difference of weighted composition operators (2008, background): “where cp 2R and jcpj is so small that � 2 maps D into D (see [ 15 ]).”
Linear relations in the Calkin algebra for composition operators (2006, unknown): “More recently, MacCluer, Ohno, and Zhao [14] have shown that compactness of Cϕ−Cψ acting on H∞, the space of bounded analytic functions on D, is characterized in terms of the quantity ρ(z) = ∣ ∣ ∣ ϕ(z)−ψ(z) 1−ϕ(z)ψ(z) ∣ ∣ ∣ , the pseudo-hyperbolic distance between values of ϕ and ψ.”