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Some applications of almost analytic extensions to operator bounds in trace ideals

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Abstract

Using the Davies-Helffer-Sjostrand functional calculus based on almost analytic extensions, we address the following problem: Given a self-adjoint operator $S$ in $\mathcal H$, and functions $f$ in an appropriate class, for instance, $f \in C_0^{\infty}(\mathbb R)$, how to control the norm $\|f(S)\|_{\mathcal B(\mathcal H)}$ in terms of the norm of the resolvent of $S$, $\|(S - z_0 I_{\mathcal H})^{-1}\|_{\mathcal B(\mathcal H)}$, for some $z_0 \in \mathbb C\backslash\mathbb R$. We are particularly interested in the case where $\mathcal B(\mathcal H)$ is replaced by a trace ideal, $\mathcal B_p(\mathcal H)$, $p \in [1,\infty)$.

Key words: Almost analytic extensions, trace ideals, operator bounds.


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Article Information

TitleSome applications of almost analytic extensions to operator bounds in trace ideals
SourceMethods Funct. Anal. Topology, Vol. 21 (2015), no. 2, 151–169
MathSciNet 3407907
zbMATH 06533473
MilestonesReceived 01/02/2015
CopyrightThe Author(s) 2015 (CC BY-SA)

Authors Information

F. Gesztesy
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA

R. Nichols
Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN 37403, USA


Citation Example

Fritz Gesztesy and Roger Nichols, Some applications of almost analytic extensions to operator bounds in trace ideals, Methods Funct. Anal. Topology 21 (2015), no. 2, 151–169.


BibTex

@article {MFAT776,
    AUTHOR = {Gesztesy, Fritz and Nichols, Roger},
     TITLE = {Some applications of almost analytic extensions to operator bounds in trace ideals},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {21},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {151–169},
      ISSN = {1029-3531},
  MRNUMBER = {3407907},
 ZBLNUMBER = {06533473},
       URL = {http://mfat.imath.kiev.ua/article/?id=776},
}


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