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On large coupling convergence within trace ideals


Let $\mathcal E$ and $\mathcal P$ be nonnegative quadratic forms such that $\mathcal E + b \mathcal P$ is closed and densely defined for every nonnegative real number $b$. Let $H_b$ be the selfadjoint operator associated with $\mathcal E + b\mathcal P.$ By Kato's monotone convergence theorem, there exists an operator $L$ such that $(H_b+1)^{-1}$ converges to $L$ strongly, as $b$ tends to infinity. We give a condition which is sufficient in order that the operators $(H_b+1)^{-1}$ converge w.r.t. the trace norm with convergence rate $O(1/b)$. As an application we discuss trace norm resolvent convergence of Schrodinger operators with point interactions.

Key words: Trace of a Dirichlet form, point interactions, quadratic form.

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TitleOn large coupling convergence within trace ideals
SourceMethods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 3-9
MathSciNet   MR3242118
zbMATH 1313.47043
Milestones  Received 05/08/2013
CopyrightThe Author(s) 2014 (CC BY-SA)

Authors Information

Johannes F. Brasche
Institute of Mathematics, TU Clausthal, Clausthal--Zellerfeld, 38678, Germany 

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Johannes F. Brasche, On large coupling convergence within trace ideals, Methods Funct. Anal. Topology 20 (2014), no. 1, 3-9.


@article {MFAT704,
    AUTHOR = {Brasche, Johannes F.},
     TITLE = {On large coupling convergence within trace ideals},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {20},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {3-9},
      ISSN = {1029-3531},
  MRNUMBER = {MR3242118},
 ZBLNUMBER = {1313.47043},
       URL = {},

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