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This paper considers two general concepts of dichotomy for noninvertible and nonautonomous linear discrete-time systems in Banach spaces. These concepts use two types of dichotomy projections sequences (invariant and strongly invariant) and generalize some well-known dichotomy concepts (uniform, nonuniform, exponential, and polynomial). In the particular caseof strongly invariant dichotomy projections, we present characterizations of these sequences and connections with other dichotomy concepts existent in the literature. Some illustrative examples clarify the implications between these concepts

international journal of differential equations

On (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:math>)-Dichotomies for Nonautonomous Linear Difference Equations in Banach Spaces

On (h,k)-Dichotomies for Nonautonomous Linear Difference Equations in Banach Spaces