TY - JOUR
T1 - Weak Lp-stability of a linear semigroup on a Hilbert space implies exponential stability
AU - Weiss, George
PY - 1988/12
Y1 - 1988/12
N2 - We prove that a strongly continuous semigroup of linear operators on a Hilbert space is weakly Lp-stable for some p ε{lunate} [1, ∞) if and only if the semigroup is exponentially stable. As an application, we prove that the Cauchy problems associated with the semigroup are well posed on the infinite time interval (- ∞, 0] if and only if the semigroup is exponentially stable.
AB - We prove that a strongly continuous semigroup of linear operators on a Hilbert space is weakly Lp-stable for some p ε{lunate} [1, ∞) if and only if the semigroup is exponentially stable. As an application, we prove that the Cauchy problems associated with the semigroup are well posed on the infinite time interval (- ∞, 0] if and only if the semigroup is exponentially stable.
UR - http://www.scopus.com/inward/record.url?scp=0000508233&partnerID=8YFLogxK
U2 - 10.1016/0022-0396(88)90075-7
DO - 10.1016/0022-0396(88)90075-7
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AN - SCOPUS:0000508233
SN - 0022-0396
VL - 76
SP - 269
EP - 285
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -