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PreprintCC0arXiv

Functions of Sp-almost commuting unitary operators and contractions. An extension of the Carey--Pincus trace formula

  • A. B. Aleksandrov
  • V. V. Peller
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Abstract

In this paper we study functions of pairs of unitary operators and pairs of contractions with commutators in the Schatten-von Neumann class Sp. We obtain commutator estimates and prove that our functional calculus is multiplicative modulo Sp. On the other hand, we show that our commutator estimates do not extend to the case p>2. We also obtain an extension of the Carey--Pincus trace formula. The main tool of this paper is a technique of triple operator integrals.

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Cite

BibTeXRIS
BibTeX
@misc{aleksandrov2026functions,
  title = {{Functions of $\boldsymbolS_p$-almost commuting unitary operators and contractions. An extension of the Carey--Pincus trace formula}},
  author = {A. B. Aleksandrov and V. V. Peller},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01149},
  eprint = {2611.01149},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01149},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Functions of S_p-almost commuting unitary operators and contractions. An extension of the Carey--Pincus trace formula
AU  - A. B. Aleksandrov
AU  - V. V. Peller
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01149
UR  - https://arxiv.org/abs/2611.01149
AB  - In this paper we study functions of pairs of unitary operators and pairs of contractions with commutators in the Schatten-von Neumann class S_p. We obtain commutator estimates and prove that our functional calculus is multiplicative modulo S_p. On the other hand, we show that our commutator estimates do not extend to the case p>2. We also obtain an extension of the Carey--Pincus trace formula. The main tool of this paper is a technique of triple operator integrals.
ER  -