LEADER 03456nam 22005175 450 001 9910360852303321 005 20200701152931.0 010 $a3-030-18877-9 024 7 $a10.1007/978-3-030-18877-1 035 $a(CKB)4100000009844901 035 $a(DE-He213)978-3-030-18877-1 035 $a(MiAaPQ)EBC5979645 035 $a(PPN)258058854 035 $a(EXLCZ)994100000009844901 100 $a20191117d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGibbs Semigroups$b[electronic resource] /$fby Valentin A. Zagrebnov 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (XVI, 320 p.) 225 1 $aOperator Theory: Advances and Applications,$x0255-0156 ;$v273 311 $a3-030-18876-0 327 $aSemigroups and their generators -- Classes of compact operators -- Trace inequalities -- Gibbs semigroups -- Product formulae for Gibbs semigroups -- Product formulae in symmetrically-normed ideals -- Product formulae in Dixmier ideal -- Appendix A. Spectra of closed operators -- Appendix B. Inequalities in ideals -- Appendix B. More inequalities -- Appendix C. Kato functions -- Appendix D. Lie-Trotter-Kato product formulae: comments on the bibliography -- Bibliography -- Index. 330 $aThis book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development. It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal. By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics. 410 0$aOperator Theory: Advances and Applications,$x0255-0156 ;$v273 606 $aOperator theory 606 $aFunctional analysis 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aOperator Theory. 615 24$aFunctional Analysis. 676 $a515.724 700 $aZagrebnov$b Valentin A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781340 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360852303321 996 $aGibbs Semigroups$91732491 997 $aUNINA