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Vietnam Journal of Mathematics 34:3(2006) 357-368  Robust Stability of Metzler Operator and Delay Equation in $L^p([-h,0];X)$ B. T. Anh, N. K. Son, and D. D. X. Thanh Abstract.  In this paper we study how the spectral bound of Mezler operator changes under multi-pertubations. Characterizations of the stability radius of Metzler operators with respect to this type of disturbances are established. We will then apply the obtained results to study the stability radius of delays equation in $L^p([-1,0],X).$   2000 Mathematics Subject Classification: 34K06, 93C73, 93D09. Keywords: Metzler operator, stability radius, $C_0$-semigroup, delay equations.

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