2022/01/18 by А. Б. Александров, Aleksandrov, Aleksei, Vladimir Peller +1
Mathematics · #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2201.07278
openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f be a function in the inhomogeneous analytic Besov space B∞,11. For a pair (L,M) of not necessarily commuting maximal dissipative operators, we define the function f(L,M) of L and M as a densely defined linear operator. We prove for p∈[1,2] that if (L1,M1) and (L2,M2) are pairs of not necessarily commuting maximal dissipative operators such that both differences L1-L2 and M1-M2 belong to the Schatten--von Neumann class \boldsymbolSp than for an arbitrary function f in the inhomogeneous analytic Besov space B∞,11, the operator difference f(L1,M1)-f(L2,M2) belongs to \boldsymbolSp and the following Lipschitz type estimate holds: ‖f(L1,M1)-f(L2,M2)‖_\boldsymbolSp \leconst‖f‖_B∞,11max\‖L1-L2‖_\boldsymbolSp,‖M1-M2‖_\boldsymbolSp\.