We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.
@article{bwmeta1.element.bwnjournal-article-smv142i1p65bwm, author = {Mats Andersson and Sebastian Sandberg}, title = {A constructive proof of the composition rule for Taylor's functional calculus}, journal = {Studia Mathematica}, volume = {141}, year = {2000}, pages = {65-69}, zbl = {0979.47014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i1p65bwm} }
Andersson, Mats; Sandberg, Sebastian. A constructive proof of the composition rule for Taylor's functional calculus. Studia Mathematica, Tome 141 (2000) pp. 65-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i1p65bwm/
[000] [1] M. Andersson, Taylor's functional calculus with Cauchy-Fantappiè-Leray formulas Internat. Math. Res. Notes 6 (1997), 247-258
[001] [2] M. Andersson, Correction to 'Taylor's functional calculus with Cauchy-Fantappiè-Leray for- mulas' ibid. 2 (1998), 123-124
[002] [3] M. Andersson and B. Berndtsson, Nonholomorphic functional calculus for several commuting operators with real spectrumin preparation
[003]
[004] [5] E. M. Dynkin, An operator calculus based on the Cauchy-Green formula Zap. Nauchn. Sem. LOMI 30 (1972), 33-40 (in Russian)
[005] [6] J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves Clarendon Press, Oxford, 1996
[006] [7] M. Putinar, The superposition property for Taylor's functional calculus J. Operator Theory 7 (1982), 149-155 | Zbl 0483.46028
[007] [8] S. Sandberg, On non-holomorphic functional calculus for commuting operatorspreprint, 1999 | Zbl 0929.47008
[008] [9] J. L. Taylor, A joint spectrum for several commuting operators J. Funct. Anal. 6 (1970), 172-191 | Zbl 0233.47024
[009] [10] J. L. Taylor, The analytic-functional calculus for several commuting operators Acta Math. 125 (1970), 1-38 | Zbl 0233.47025
[010] [11] J. L. Taylor, Homology and cohomology for topological algebras Adv. Math. 9 (1972), 137-182 | Zbl 0271.46040
[011] [12] J. L. Taylor, A general framework for a multi-operator functional calculus ibid., 184-252