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Operators on Differential Form Spaces for Riemann Surfaces

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Abstract

In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator C p is Fredholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the Toeplitz operators on \( \Lambda _{2,a}^1 (M) \)for Riemann surface M are defined and some properties of these operators are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Guangzhou University, Guangzhou 510405, P. R. China

    Guang Fu Cao & Xiao Feng Wang

Authors
  1. Guang Fu Cao
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  2. Xiao Feng Wang
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Correspondence to Guang Fu Cao.

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Supported partially by National Natural Science Foundation of China

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Cao, G.F., Wang, X.F. Operators on Differential Form Spaces for Riemann Surfaces. Acta Math Sinica 23, 925–934 (2007). https://doi.org/10.1007/s10114-005-0846-4

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  • DOI: https://doi.org/10.1007/s10114-005-0846-4

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