Composition operators on some Möbius invariant Banach spaces

Shamil Makhmutov, Maria Tjani

Research output: Contribution to journalArticle

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

Fingerprint

Composition Operator
Compact Operator
Bloch Space
Banach space
Invariant
Hyperbolic function
Möbius
Unit Disk
Analytic function
Oscillation
If and only if

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Composition operators on some Möbius invariant Banach spaces. / Makhmutov, Shamil; Tjani, Maria.

In: Bulletin of the Australian Mathematical Society, Vol. 62, No. 1, 08.2000, p. 1-19.

Research output: Contribution to journalArticle

@article{7836d8410db146c1896677ecd65deb00,
title = "Composition operators on some M{\"o}bius invariant Banach spaces",
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.",
author = "Shamil Makhmutov and Maria Tjani",
year = "2000",
month = "8",
language = "English",
volume = "62",
pages = "1--19",
journal = "Bulletin of the Australian Mathematical Society",
issn = "0004-9727",
publisher = "Cambridge University Press",
number = "1",

}

TY - JOUR

T1 - Composition operators on some Möbius invariant Banach spaces

AU - Makhmutov, Shamil

AU - Tjani, Maria

PY - 2000/8

Y1 - 2000/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040212692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040212692&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040212692

VL - 62

SP - 1

EP - 19

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 1

ER -