An extension of the Koplienko-Neidhardt trace formulae

By V. Peller. 2004

47 citations recorded by the source corpus.

Koplienko [Ko] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert Schmidt class $\bS_2$. A similar formula in the case of unitary operators was obtained by Neidhardt [N]. In this paper we improve their results and obtain sharp conditions under which the Koplienko--Neidhardt trace formulae hold.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f5259ae63f6b6a2a26edcea5c55d8bd12fb0286b

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In Applied Mathematics

1. D. Potapov
2. Fedor Sukochev
3. V. Peller
4. A. Skripka
5. Richard C. Bradley
6. Sandrine Grellier
7. Gregory Beylkin
8. Lucas Monzón

In Computational Theory and Mathematics

1. Fedor Sukochev
2. D. Potapov
3. A. Skripka

In Mathematical Physics

1. D. Potapov
2. V. Peller
3. Fedor Sukochev
4. A. Skripka
5. Alan L. Carey

Citations in the corpus

• Multiple operator integrals and higher operator derivatives (2005, background): “ perturbations (see [Pe1] and [Pe2]), while the Besov spaces B2 ∞1 and B 2 ∞1(R) arise when studying the applicability of the Koplienko–Neidhardt trace formulae for Hilbert–Schmidt perturbations (see [Pe5]). It is also interesting to note that the Besov class B2 ∞1(R) appears in a natural way in per”
• Spectral shift function of higher order (2009, background): “7) for n = 1 was obtained in [1, 15] and for n = 2 in [19].”
• Multiple operator integrals in perturbation theory (2015, background): “1) was generalized in [56] to the case when f is an arbitrary function in the Besov class B2 ∞,1(R).”