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＜電子ブック＞
Gibbs Semigroups / by Valentin A. Zagrebnov
(Operator Theory: Advances and Applications. ISSN:22964878 ; 273)

版	1st ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2019
大きさ	XVI, 320 p : online resource
著者標目	*Zagrebnov, Valentin A author SpringerLink (Online service)
件　名	LCSH:Operator theory LCSH:Functional analysis FREE:Operator Theory FREE:Functional Analysis
一般注記	Semigroups 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 This 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 HTTP:URL=https://doi.org/10.1007/978-3-030-18877-1

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