caa a22 4500 445345217 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00233-011-9348-0 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9348-0 On exponential stability of contraction semigroups [Elektronische Daten] [Carlos Kubrusly, Nhan Levan] A semigroup [T(t)] on a Hilbert space is exponentially stable if there exist real constants M≥1 and α>0 such that ∥T(t)∥≤Me −αt for every t≥0. If [T(t)] is a strongly continuous contraction semigroup, then it is proved that we can set M=1 in the definition of exponential stability if and only if the generator A of [T(t)] is boundedly strict dissipative (just a strict dissipative A is not enough). Springer Science+Business Media, LLC, 2011 Hilbert space contraction semigroups nationallicence Exponential stability nationallicence Kubrusly Carlos Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil aut Levan Nhan Department of Electrical Engineering, University of California in Los Angeles, 90024-1594, Los Angeles, CA, USA aut Semigroup Forum Springer-Verlag 83/3(2011-12-01), 513-521 0037-1912 83:3<513 2011 83 233 https://doi.org/10.1007/s00233-011-9348-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9348-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kubrusly Carlos Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil aut NATIONALLICENCE 700 1- Levan Nhan Department of Electrical Engineering, University of California in Los Angeles, 90024-1594, Los Angeles, CA, USA aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/3(2011-12-01), 513-521 0037-1912 83:3<513 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer