The aim of this paper is to develop a framework for a unitary approach in a nonuniform setting for various concepts of dichotomy for skew-evolution semiflows on infinite dimensional spaces. The techniques that describe the stability and instability in infinite dimensional spaces are improved to characterize the property of dichotomy. Beside the classic concepts of uniform exponential dichotomy and exponential dichotomy, we propose also the notions of Barreira-Valls exponential dichotomy and (h, k)–dichotomy. Connections between notions are pointed out, several examples and counter examples underlining the statements.
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