Differentiable $L^p$-functional calculus for certain sums of non-commuting operators
Volume 105 / 2006
Colloquium Mathematicum 105 (2006), 105-125
MSC: Primary 47A60, 47B25; Secondary 22E25, 22E30.
DOI: 10.4064/cm105-1-10
Abstract
We consider a special class of sums of non-commuting positive operators on $L^2$-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable $L^p$-functional calculus for $1\leq p \leq \infty $. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.
