Acta mathematica scientia,Series B ›› 1994, Vol. 14 ›› Issue (1): 95-99.
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Song Guozhu
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Abstract: Let S(t), t ≥ 0, be a strongly continuous semigroup on a Banach space, with infinitesimal generator A. The main results are as follows:Let either S(t) or S* (t) be uniformly stable as t → + ∞, yet not uniformly exponentially stable as t →+ ∞. Then for any compact operator B on X, the semigroup SB(t) generated by A+B cannot be uniformly exponentially stable as t→ + ∞. This result improves a result in[2] and[3], removing the assumption that S(t) is a contraction and X is a Hilbert space.
Song Guozhu. A NOTE OF UNIFORM EXPONENTIAL STABILIZATION FOR NONCONTRACTIVE SEMIGROUPS UNDER COMPACT PERTURBATION[J].Acta mathematica scientia,Series B, 1994, 14(1): 95-99.
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