Composition operators on some Möbius invariant Banach spaces

Shamil Makhmutov, Maria Tjani

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20 Citations (Scopus)

Abstract

We characterise the compact composition operators from any Mobius invariant Banach space to VMOA, the space of holomorphic functions on the unit disk U that have vanishing mean oscillation. We use this to obtain a characterisation of the compact composition operators from the Bloch space to VMOA. Finally, we study some properties of hyperbolic VMOA functions. We show that a function is hyperbolic VMOA if and only if it is the symbol of a compact composition operator from the Bloch space to VMOA.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalBulletin of the Australian Mathematical Society
Volume62
Issue number1
Publication statusPublished - Aug 2000

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ASJC Scopus subject areas

  • Mathematics(all)

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