2001
DOI: 10.1007/bf01198142
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Topological structure of the space of composition operators onH ?

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Cited by 110 publications
(101 citation statements)
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“…However, it is not compact, since w(r ) v(φ(r )) ρ(φ(r ), ψ(r )) = 8 (1 − r ) 2 t (r − 1) 3 For examples of compact and noncompact differences of composition operators C φ − C ψ : H ∞ → H ∞ , see [19,Example 1]. The change of the behaviour of the operator C φ − C ψ depending on the weights v and w is emphasized in our last example.…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…However, it is not compact, since w(r ) v(φ(r )) ρ(φ(r ), ψ(r )) = 8 (1 − r ) 2 t (r − 1) 3 For examples of compact and noncompact differences of composition operators C φ − C ψ : H ∞ → H ∞ , see [19,Example 1]. The change of the behaviour of the operator C φ − C ψ depending on the weights v and w is emphasized in our last example.…”
Section: Resultsmentioning
confidence: 99%
“…The case of operators defined on weighted Banach spaces of the type defined above was treated, for example, in [4,5] and [6]. Differences of composition operators have been investigated more recently; see [10,13,14,19] and [20]. In this article we are mainly interested in finding an expression for the essential norm C φ − C ψ e , that is, the distance of C φ − C ψ to the space of compact operators, when C φ − C ψ is a bounded operator from H ∞ v into H ∞ w ; compare with [10] and [12] for the case of H ∞ .…”
Section: Introductionmentioning
confidence: 99%
“…Hence C ϕ1 − C ϕ2 e = 0. By [12,Theorem 3], lim z→1 ρ(ϕ 1 (z), ϕ 2 (z)) = 0. By Theorem 2.5, C ϕ1 − C ϕ2 < 2.…”
Section: Examplesmentioning
confidence: 99%
“…Recently, the norm, the essential norm and the topological structure of composition operators on H ∞ have been studied (see [5,6,8,9,10,12]). But the exact value of the essential norm of the difference of composition operators C ϕ −C ψ e on H ∞ is not yet known.…”
Section: Introductionmentioning
confidence: 99%
“…Composition operators and weighted composition operators acting between various spaces of analytic functions have been investigated by several authors (see e.g. [13], [7], [11], [2], [4], [3], [8], [12]). In [13] and [12] weighted composition operators between weighted Bloch type spaces resp.…”
mentioning
confidence: 99%