JournalsowrVol. 1 / No. 3DOI 10.4171/owr/2004/36

Spectral Theory in Banach Spaces and Harmonic Analysis

  • Alan G.R. McIntosh

    Australian National University, Canberra, Australia
  • Nigel Kalton

    University of Missouri, Columbia, USA
  • Lutz Weis

    Universität Karlsruhe, Germany
Spectral Theory in Banach Spaces and Harmonic Analysis cover

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Abstract

The conference was motivated by the recent solutions of two longstanding questions. The first one is Kato's square root problem, i.e.~whether for an elliptic operator in divergence form on we have for . After a long development over 40 years this was shown in a joint effort by P.~Auscher, S.~Hofmann, M.~Lacey, A.~McIntosh and Ph.~Tchamitchian. For a new approach to this important result via Dirac operators and extensions of it, see the abstracts of A.~McIntosh and S.~Keith. The second problem, attributed to Br{\'e}zis in the eighties, asks whether the Cauchy problem for every generator of an analytic semigroup in an -space with $1