# A constructive proof of the composition rule for Taylor's functional calculus

Mats Andersson; Sebastian Sandberg

Studia Mathematica (2000)

- Volume: 142, Issue: 1, page 65-69
- ISSN: 0039-3223

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topAndersson, Mats, and Sandberg, Sebastian. "A constructive proof of the composition rule for Taylor's functional calculus." Studia Mathematica 142.1 (2000): 65-69. <http://eudml.org/doc/216789>.

@article{Andersson2000,

abstract = {We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.},

author = {Andersson, Mats, Sandberg, Sebastian},

journal = {Studia Mathematica},

keywords = {Taylor spectrum; functional calculus; Cauchy-Fantappiè-Leray formula; abstract Cauchy-Fantappiè-Lerey kernel; joint spectrum},

language = {eng},

number = {1},

pages = {65-69},

title = {A constructive proof of the composition rule for Taylor's functional calculus},

url = {http://eudml.org/doc/216789},

volume = {142},

year = {2000},

}

TY - JOUR

AU - Andersson, Mats

AU - Sandberg, Sebastian

TI - A constructive proof of the composition rule for Taylor's functional calculus

JO - Studia Mathematica

PY - 2000

VL - 142

IS - 1

SP - 65

EP - 69

AB - We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.

LA - eng

KW - Taylor spectrum; functional calculus; Cauchy-Fantappiè-Leray formula; abstract Cauchy-Fantappiè-Lerey kernel; joint spectrum

UR - http://eudml.org/doc/216789

ER -

## References

top- [1] M. Andersson, Taylor's functional calculus with Cauchy-Fantappiè-Leray formulas Internat. Math. Res. Notes 6 (1997), 247-258
- [2] M. Andersson, Correction to 'Taylor's functional calculus with Cauchy-Fantappiè-Leray for- mulas' ibid. 2 (1998), 123-124
- [3] M. Andersson and B. Berndtsson, Nonholomorphic functional calculus for several commuting operators with real spectrumin preparation
- [5] E. M. Dynkin, An operator calculus based on the Cauchy-Green formula Zap. Nauchn. Sem. LOMI 30 (1972), 33-40 (in Russian)
- [6] J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves Clarendon Press, Oxford, 1996
- [7] M. Putinar, The superposition property for Taylor's functional calculus J. Operator Theory 7 (1982), 149-155 Zbl0483.46028
- [8] S. Sandberg, On non-holomorphic functional calculus for commuting operatorspreprint, 1999 Zbl0929.47008
- [9] J. L. Taylor, A joint spectrum for several commuting operators J. Funct. Anal. 6 (1970), 172-191 Zbl0233.47024
- [10] J. L. Taylor, The analytic-functional calculus for several commuting operators Acta Math. 125 (1970), 1-38 Zbl0233.47025
- [11] J. L. Taylor, Homology and cohomology for topological algebras Adv. Math. 9 (1972), 137-182 Zbl0271.46040
- [12] J. L. Taylor, A general framework for a multi-operator functional calculus ibid., 184-252

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