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Toeplitz and Hankel operators between distinct Hardy spaces

Volume 249 / 2019

Karol Leśnik Studia Mathematica 249 (2019), 163-192 MSC: Primary 47B35; Secondary 46E30, 30H10. DOI: 10.4064/sm180207-9-7 Published online: 31 May 2019

Abstract

The paper deals with Toeplitz and Hankel operators acting between distinct Hardy type spaces over the unit circle $\mathbb {T}$. We characterize possible symbols of such operators and prove general versions of the Brown–Halmos theorem and the Nehari theorem. A lower bound for the Kuratowski measure of noncompactness of a Toeplitz operator is also found. Our approach allows handling Hardy spaces associated with arbitrary rearrangement invariant spaces, but the main part of the results are new even for the classical $H^p$ spaces.

Authors

  • Karol LeśnikInstitute of Mathematics
    Poznań University of Technology
    Piotrowo 3a
    60-965 Poznań, Poland
    e-mail

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