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# On large coupling convergence within trace ideals

### Abstract

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.

### Article Information

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

### Authors Information

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

### Citation Example

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

### BibTex

@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 = {http://mfat.imath.kiev.ua/article/?id=704},
}