Some applications of almost analytic extensions to operator bounds in trace ideals
DOI:
Keywords:
Almost analytic extensions, trace ideals, operator boundsAbstract
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, $\mathcal B_p(\mathcal H)$, $p \in [1,\infty)$.References
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