Mustafayev, Heybetkulu2025-05-102025-05-1020070022-123610.1016/j.jfa.2007.02.0042-s2.0-34249665653https://doi.org/10.1016/j.jfa.2007.02.004https://hdl.handle.net/20.500.14720/12471A bounded linear operator T on a Banach space is said to be dissipative if parallel to e(tT)parallel to <= 1 for all t >= 0. We show that if T is a dissipative operator on a Banach space, then: (a)lim(t)->infinity parallel to e(tT) T parallel to = {vertical bar lambda vertical bar: lambda epsilon sigma (T) boolean AND i R} (b) If sigma (T) boolean AND i R is contained in [-i pi/2, i pi/2], then [GRAPHICS] Some related problems are also discussed. (c) 2007 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/openAccessHermitian OperatorDissipative Operator(Local) SpectrumFourier TransformArticle2482Q1Q1428447WOS:000247706100006