Higher order S2-differentiability and application to Koplienko trace formula
| Autor: | Anna Skripka, Christian Le Merdy, Clément Coine, Fedor Sukochev |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Mathematics::Operator Algebras 010102 general mathematics Hilbert space 01 natural sciences symbols.namesake Factorization Bounded function Norm (mathematics) 0103 physical sciences symbols 010307 mathematical physics Differentiable function 0101 mathematics Analysis Separable hilbert space Mathematics |
| Zdroj: | Journal of Functional Analysis. 276:3170-3204 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2018.09.005 |
| Popis: | Let A be a selfadjoint operator in a separable Hilbert space, K a selfadjoint Hilbert–Schmidt operator, and f ∈ C n ( R ) . We establish that φ ( t ) = f ( A + t K ) − f ( A ) is n-times continuously differentiable on R in the Hilbert–Schmidt norm, provided either A is bounded or the derivatives f ( i ) , i = 1 , … , n , are bounded. This substantially extends the results of [3] on higher order differentiability of φ in the Hilbert–Schmidt norm for f in a certain Wiener class. As an application of the second order S 2 -differentiability, we extend the Koplienko trace formula from the Besov class B ∞ 1 2 ( R ) [20] to functions f for which the divided difference f [ 2 ] admits a certain Hilbert space factorization. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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