manuscripta mathematica

, Volume 59, Issue 4, pp 399–422 | Cite as

Operatoren H1→X

  • Wolfgang Hensgen


Let X be a complex Banach space and H1 the usual Hardy space. Various properties of operators L1/H 0 1 →X and, mainly, H1→X are considered, e.g. being weakly compact, Riesz representable, Dunford-Pettis. Connections with RNP resp. aRNP and with the validity of the equation\(H^1 \widehat \otimes X \cong \mathbb{H}^1 \left( X \right)\) are also studied, the latter space being an X-valued Hardy space. Whereas results for operators L1/H 0 1 →X closely resemble well-known theorems about operators L1→ X, this is not the case for operators H1→X. E.g., for “most” classical Banach spaces X it isnot true that\(H^1 \widehat \otimes X \cong \mathbb{H}^1 \left( X \right)\) (canonically).


Banach Space Number Theory Algebraic Geometry Hardy Space Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Wolfgang Hensgen
    • 1
  1. 1.NWF I-MathematikUniversität RegensburgRegensburg

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