The aim of the present paper is to give two characterization theorems of Datko type for the nonuniform polynomial dichotomy concept with respect to invariant projection families and also with respect to strongly invariant projection families.

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The aim of the present paper is to emphasize some growth concepts for the dichotomic behavior of evolution operators in Banach spaces. In fact, we approach the exponential growth, the polynomial growth and the h-growthfor both uniform and nonuniform cases. Connections between concepts are established. Majorization criteria for the uniform behaviors are given.