Abstract: The exponential φ-expansiveness of linear skew-product semiflows in Banach space was studied. Based on the definition of uniform exponential expansiveness, a linear skew-product semiflow with exponential φ-expansiveness was presented. Some characterizations for exponential φ-expansiveness were obtained via mathematical analysis and operator theory. The results extend some well-known conclusions in the exponential stability theory.

Key words: linear skew-product semiflows, exponential φ-expansiveness, function spaces