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 HAL: hal-00700159, version 1
 Available versions: v1 (2012-05-22) v2 (2012-06-25)
 The Weiss conjecture and weak norms
 (2012-05-22)
 In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators $Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0$ on the complex right half plane and weak Lebesgue $L^{2,\infty}$--admissibility are equivalent. Moreover, we show that the weak Lebesgue norm is best possible in the sense that it is the endpoint for the 'Weiss conjecture' within the scale of Lorentz spaces $L^{p,q}$.
 1: Institut de Mathématiques de Bordeaux (IMB) CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
 Subject : Mathematics/Functional AnalysisMathematics/Optimization and Control
 Keyword(s): Observation of linear systems – Weiss conjecture – Lorentz spaces
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 hal-00700159, version 1 http://hal.archives-ouvertes.fr/hal-00700159 oai:hal.archives-ouvertes.fr:hal-00700159 From: Bernhard Hermann Haak <> Submitted on: Tuesday, 22 May 2012 14:34:58 Updated on: Tuesday, 22 May 2012 14:48:28