3 results
ORDER BOUNDED WEIGHTED COMPOSITION OPERATORS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 93 / Issue 3 / December 2012
- Published online by Cambridge University Press:
- 09 April 2013, pp. 333-343
- Print publication:
- December 2012
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Let
$\phi $ and 
$\psi $ be analytic maps on the open unit disk 
$D$ such that 
$\phi (D) \subset D$. Such maps induce a weighted composition operator 
$C_{\phi ,\psi }$ acting on weighted Banach spaces of type 
$H^{\infty }$or on weighted Bergman spaces, respectively. We study when such operators are order bounded.
DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 84 / Issue 1 / February 2008
- Published online by Cambridge University Press:
- 01 February 2008, pp. 9-20
- Print publication:
- February 2008
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We consider differences of composition operators between given weighted Banach spaces
or Hv0 of analytic functions with weighted sup-norms and give estimates for the distance of these differences to the space of compact operators. We also study boundedness and compactness of the operators. Some examples illustrate our results.
or Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions
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- Journal:
- Canadian Mathematical Bulletin / Volume 42 / Issue 2 / 01 June 1999
- Published online by Cambridge University Press:
- 20 November 2018, pp. 139-148
- Print publication:
- 01 June 1999
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Every weakly compact composition operator between weighted Banach spaces
$H_{v}^{\infty }$ of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space $H_{v}^{\infty }$ are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.
