TY - JOUR

T1 - Real-Valued Spectral Shift Functions for Contractions and Dissipative Operators

AU - Маламуд, Марк Михайлович

AU - Найдхардт, Хаген

AU - Пеллер, Владимир Всеволодович

PY - 2024/11/11

Y1 - 2024/11/11

N2 - Abstract: In recent joint papers the authors of this note solved a famous problem remained open for many years and proved that for arbitrary contractions with trace class difference there exists an integrable spectral shift function, for which an analogue of the Lifshits–Krein trace formula holds. Similar results were also obtained for pairs of dissipative operators. Note that in contrast with the case of self-adjoint and unitary operators it may happen that there is no real-valued integrable spectral shift function. In this note we announce results that give sufficient conditions for the existence of an integrable real-valued spectral shift function in the case of pairs of contractions. We also consider the case of pairs of dissipative operators.

AB - Abstract: In recent joint papers the authors of this note solved a famous problem remained open for many years and proved that for arbitrary contractions with trace class difference there exists an integrable spectral shift function, for which an analogue of the Lifshits–Krein trace formula holds. Similar results were also obtained for pairs of dissipative operators. Note that in contrast with the case of self-adjoint and unitary operators it may happen that there is no real-valued integrable spectral shift function. In this note we announce results that give sufficient conditions for the existence of an integrable real-valued spectral shift function in the case of pairs of contractions. We also consider the case of pairs of dissipative operators.

UR - https://www.mendeley.com/catalogue/5258a5cb-a1f4-3003-a77e-f7fdd42f7da9/

U2 - 10.1134/S1064562424601203

DO - 10.1134/S1064562424601203

M3 - Article

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

ER -