Geodesic
Differentiable $L^p$-functional calculus for certain sums of non-commuting operators
Michael Gnewuch1
1 Max Planck Institute for Mathematics in the Sciences Inselstr. 22 D-04103 Leipzig, Germany
Colloquium Mathematicum, Tome 105 (2006) no. 1, pp. 105-125

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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.
DOI : 10.4064/cm105-1-10
Keywords: consider special class sums non commuting positive operators spaces derive formula their holomorphic semigroups formula enables sufficient conditions these operators admit differentiable p functional calculus leq leq infty results particular applicable certain sub laplacians schr dinger operators sums even powers vector fields solvable lie groups exponential volume growth

Michael Gnewuch 1

1 Max Planck Institute for Mathematics in the Sciences Inselstr. 22 D-04103 Leipzig, Germany 
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Michael Gnewuch. Differentiable $L^p$-functional calculus for certain
 sums of non-commuting operators. Colloquium Mathematicum, Tome 105 (2006) no. 1, pp. 105-125. doi: 10.4064/cm105-1-10

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