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The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated ℒp spaces, with p∈(1,∞], is admissible for a given evolution process, then this process is a nonuniform (μ,ν) contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform (μ,ν) contractionand dichotomy is provided

abstract and applied analysis

Admissibility for Nonuniform<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:mi>ν</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>Contraction and Dichotomy

Admissibility for Nonuniform(μ,ν)Contraction and Dichotomy