Functions of self-adjoint operators in ideals of compact operators

Abstract

For self-adjoint operators $A,B$, a bounded operator $J$, and a function $f:\mathbb{R}\to \mathbb{C}$ we obtain bounds in quasi-normed ideals of compact operators for the difference $f(A)J-Jf(B)$ in terms of the operator $AJ-JB$. The focus is on functions $f$ that are smooth everywhere except for finitely many points. A typical example is the function $f(t)=|t{|}^{\gamma }$ with $\gamma \in (0,1)$. The obtained results are applied to derive a two-term quasi-classical asymptotic formula for the trace $trf(S)$ with $S$ being a Wiener-Hopf operator with a discontinuous symbol.

23 pages

References in corpus (2)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Some applications of almost analytic extensions to operator bounds in trace ideals

Cited by in corpus (10)

• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
• Rényi entropies of the free Fermi gas in multi-dimensional space at high temperature
• Trace formulas for Wiener--Hopf operators with applications to entropies of free fermionic equilibrium states
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• Operator $\theta$-Hölder functions with respect to ${\Vert \cdot \Vert }_p$, $0<p\le \infty$
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator
• A Szegő limit theorem for translation-invariant operators on polygons
• Fractional powers on noncommutative $L_p$ for $p<1$
• On the Szegő formulas for truncated Wiener-Hopf operators