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2 results

  • ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE

  • Part of
  • ROBERT F. ALLEN, FLAVIA COLONNA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 79 / Issue 1 / February 2009
    Published online by Cambridge University Press:
    09 February 2009, pp. 147-160
    Print publication:
    February 2009
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  • In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

  • The Essential Norm of a Bloch-to-${{Q}_{p}}$ Composition Operator

  • Mikael Lindstróm, Shamil Makhmutov, Jari Taskinen
  • Journal:
    Canadian Mathematical Bulletin / Volume 47 / Issue 1 / 01 March 2004
    Published online by Cambridge University Press:
    20 November 2018, pp. 49-59
    Print publication:
    01 March 2004
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  • The ${{Q}_{p}}$ spaces coincide with the Bloch space for $p\,>\,1$ and are subspaces of $\text{BMOA}$ for $0\,<\,p\,\le \,1$. We obtain lower and upper estimates for the essential norm of a composition operator from the Bloch space into ${{Q}_{p}}$, in particular from the Bloch space into $\text{BMOA}$.