DOI

We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function f on R2, for which the map (A, B)↦f(A, B) is Lipschitz in the operator norm and in Schatten-von Neumann norms Sp. It turns out that for functions f in the Besov class B∞,11(R2), the above map is Lipschitz in the Sp norm for p∈[1, 2]. However, it is not Lipschitz in the operator norm, nor in the Sp norm for p>2. The main tool is triple operator integrals. To obtain the results, we introduce new Haagerup-like tensor products of L spaces and obtain Schatten-von Neumann norm estimates of triple operator integrals. We also obtain similar results for functions of noncommuting unitary operators.

Язык оригиналаанглийский
Страницы (с-по)1-52
Число страниц52
ЖурналAdvances in Mathematics
Том295
DOI
СостояниеОпубликовано - 4 июн 2016
Опубликовано для внешнего пользованияДа

    Предметные области Scopus

  • Математика (все)

ID: 87316715