Abstract
We prove that if a bounded linear operator A on a Banach space X is such that, for any x ∊ X and any y ∊ X∗, the sequence 〈Ak.x,y,〉 is in; is in lp, where p ∊ (1, ∞), then the spectral radius of A is smaller than one. This solves the discrete-time version of a problem raised by Pritchard and Zabczyk (1983). As a consequence, if the linear time-invariant discrete-time systems associated with A are lq-input-bounded state stable, where q∊(1,∞), then A is power stable.
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