On Error Estimates For The Trotter-kato Product Formula
Estimates for the Trotter–Kato Product FormulaAuthorsAuthors and affiliationsH. NeidhardtV. A. ZagrebnovArticleDOI: 10.1023/A:1007494816401Cite this article as: Neidhardt, H. & Zagrebnov, V.A. Letters in Mathematical Physics (1998) 44: 169. doi:10.1023/A:1007494816401AbstractWe study the error bound in the operator-norm topology for the Trotter exponential product formula as well as for its generalization à la Kato. Within the framework of an abstract setting, we give a simple proof of error estimates which improve some recent results in this direction.Trotter–Kato product formulaself-adjoint operatorsoperator-norm estimates.References1.Chernoff, P. R.: Note on product formulas for operator semigroups, J. Funct. Anal. 2(1968), 238-242.Google Scholar2.Chernoff, P. R.: Product formulas, nonlinear semigroups and addition of unbounded operators, Mem. Amer. Math. Soc. 140(1974), 1-121.Google Scholar3.Ichinose, T. and Tamura, H.: Error estimate in operator norm for Trotter-Kato product formula, Integral Equations Operator Theory 27(1997), 195-207.Google Scholar4.Ichinose, T. and Tamura, H.: Error bound in Trace norm for Trotter-Kato product formula of Gibbs semigroups, to appear in Asymptotic Anal.5.Kato, T: On the Trotter-Lie product formula, Proc. Japan. Acad. 50(1974), 694-698.Google Scholar6.Kato, T.: Trotter's product formula for an arbitrary pair of self-adjoint contraction semigroups, in: I. Gohberg and M. Kac (eds), Topics in Functional Analysis, Adv. Math. Suppl. Studies 3, Academic Press, New York, 1978, pp. 185-195.Google Scholar7.Neidhardt, H. and Zagrebnov, V. A.: The Trotter-Kato product formula for Gibbs semigroups, Comm. Math. Phys. 131(1990), 333-346.Google Scholar8.Reed, M. and Simon, B.: Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, New York, 1972.Google Scholar9.Rogava, D. L.: Error bounds for Trotter-type formulas for self-adjoint operators, Funct. Anal. Appl. 27(3) (1993), 217-219.Google Scholar10.Trotter, H. F.: On the products of semigroups of operators, Proc. Amer. Math. Soc. 10(1959), 545-551.Google Sc
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loginOther institution loginHelpJournalsBooksRegisterSign inHelpcloseSign in using your ScienceDirect credentialsUsernamePasswordRemember meForgotten username or password?Sign in via your institutionOpenAthens loginOther institution login Download full text in PDF Article Article http://www.sciencedirect.com/science/article/pii/S0022123699934353 + other articles in this issue Loading... Export You have selected https://books.google.de/books?id=M_PICgAAQBAJ&pg=PA89&lpg=PA89&dq=on+error+estimates+for+the+trotter-kato+product+formula&source=bl&ots=X0n9YlZO8z&sig=3qLylI-rCO1lMAJXBJ3pmIZwq7U&hl=en&sa=X&ved=0ahUKEwiKg_2yjePPAhWkA8AK 1 citation for export. Help Direct export Save to Mendeley Save to RefWorks Export file Format RIS (for EndNote, ReferenceManager, ProCite) BibTeX Text Content Citation Only Citation and Abstract Export Advanced search Close This document does not have an outline. JavaScript is on error disabled on your browser. Please enable JavaScript to use all the features on this page. Journal of Functional Analysis Volume 167, Issue 1, 10 September 1999, Pages 113-147 Regular ArticleTrotter–Kato Product Formula and Symmetrically Normed Ideals ☆ Author links open the overlay panel. Numbers correspond to the affiliation list which can be exposed by on error estimates using the show more link. Opens overlay H Neidhardt , Opens overlay V.A Zagrebnov Centre de Physique Théorique, ‡‡Unité Propre de Recherche 7061., CNRS Luminy, Case 907, F-13288, Marseille Cedex 9, France Received 4 December 1998, Accepted 22 April 1999, Available online 27 March 2002 Show more doi:10.1006/jfan.1999.3435 Get rights and content Under an Elsevier user license Open Archive AbstractIt is proven that the Trotter product formula converges in the norm of a symmetrically normed ideal of compact operators away from t0>0 if the Kac operator (the transfer matrix) F(t)=e−tB/2e−tAe−tB/2 belongs to this ideal for t=t0. The result is generalized to the Trotter–Kato product formula. Moreover, if the perturbation B is small relative to A, then error bounds for convergence are obtained. The results apply to the Dixmier trace. Keywords Trotter–Kato product formula; self-adjoint operators; convergence in symmetrically normed ideals Download full text in PDF References REFERENCES 1 H. Araki Golden–Thompson and Peierls–Bogolubov inequalities for a general vo
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