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Trotter–Kato Product Formula and Symmetrically Normed Ideals

✍ Scribed by H Neidhardt; V.A Zagrebnov

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
224 KB
Volume
167
Category
Article
ISSN
0022-1236

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✦ Synopsis

It is proven that the Trotter product formula converges in the norm of a symmetrically normed ideal of compact operators away from t 0 >0 if the Kac operator (the transfer matrix) F(t)=e &tBÂ2 e &tA e &tBÂ2 belongs to this ideal for t=t 0 . 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.

📜 SIMILAR VOLUMES

Some Remarks on Operator-Norm Convergenc
Some Remarks on Operator-Norm Convergence of the Trotter Product Formula on Banach Spaces
✍ Sönke Blunck 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 206 KB

We extend the Trotter-Kato-Chernoff theory of strong approximation of C 0 semigroups on Banach spaces to operator-norm approximation of analytic semigroups with error estimate. As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with