Abstract:
Let f be a function belonging to the nonhomogeneous analytic Besov space
(Б1∞,1)+(R2).
For a pair (L,M) of not necessarily commuting maximal dissipative
operators, the function f(L,M) is introduced as a densely defined
linear.
For p∈[1,2], we prove that if (L1,M1) and (L2,M2) are pairs of
not necessarily commuting maximal dissipative operators such that the two
difeerences L1−L2 и M1−M2
belong to the Schatten–von Neumann class Sp, then for every f in
(Б1∞,1)+(R2) the operator difference f(L1,M1)−f(L2,M2) belongs to
Sp and the following Lipschitz-type estimate holds true:
‖f(L1,M1)−f(L2,M2)‖Sp⩽const‖f‖Б1∞,1max{‖L1−L2‖Sp,‖M1−M2‖Sp}.
Keywords:
dissipative operator, Haagerup tensor product, Haagerup-type tensor products, semispectral measure, Besov classes, functions of noncommuting operators, Lipschitz-type estimates for functions of operators, Schatten–von Neumann classes.
Citation:
A. B. Aleksandrov, V. V. Peller, “Functons of perturbed pairs of noncommuting dissipative operator”, Algebra i Analiz, 34:3 (2022), 93–114; St. Petersburg Math. J., 34:3 (2023), 379–392