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3 results

  • LINEAR SURJECTIVE ISOMETRIES BETWEEN VECTOR-VALUED FUNCTION SPACES

  • Part of
  • KAZUHIRO KAWAMURA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 100 / Issue 3 / June 2016
    Published online by Cambridge University Press:
    27 January 2016, pp. 349-373
    Print publication:
    June 2016
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  • We prove some Banach–Stone type theorems for linear isometries of vector-valued continuous function spaces, by making use of the extreme point method.

  • New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk

  • Zhong-Shan Fang, Ze-Hua Zhou
  • Journal:
    Canadian Mathematical Bulletin / Volume 57 / Issue 4 / 01 December 2014
    Published online by Cambridge University Press:
    20 November 2018, pp. 794-802
    Print publication:
    01 December 2014
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  • We give some new characterizations for compactness of weighted composition operators $u{{C}_{\varphi }}$ acting on Bloch-type spaces in terms of the power of the components of $\varphi$, where $\varphi$ is a holomorphic self-map of the polydisk ${{\mathbb{D}}^{n}}$, thus generalizing the results obtained by Hyvärinen and Lindström in 2012.

  • THE ESSENTIAL NORM OF A WEIGHTED COMPOSITION OPERATOR FROM THE BLOCH SPACE TO H∞

  • Part of
  • TAKUYA HOSOKAWA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 79 / Issue 3 / June 2009
    Published online by Cambridge University Press:
    05 May 2009, pp. 487-497
    Print publication:
    June 2009
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  • We express the operator norm of a weighted composition operator which acts from the Bloch space ℬ to H∞ as the supremum of a quantity involving the weight function, the inducing self-map, and the hyperbolic distance. We also express the essential norm of a weighted composition operator from ℬ to H∞ as the asymptotic upper bound of the same quantity. Moreover we study the estimate of the essential norm of a weighted composition operator from H∞ to itself.