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

Abstract

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

How to cite

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Andersson, 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

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  1. [1] M. Andersson, Taylor's functional calculus with Cauchy-Fantappiè-Leray formulas Internat. Math. Res. Notes 6 (1997), 247-258 
  2. [2] M. Andersson, Correction to 'Taylor's functional calculus with Cauchy-Fantappiè-Leray for- mulas' ibid. 2 (1998), 123-124 
  3. [3] M. Andersson and B. Berndtsson, Nonholomorphic functional calculus for several commuting operators with real spectrumin preparation 
  4.  
  5. [5] E. M. Dynkin, An operator calculus based on the Cauchy-Green formula Zap. Nauchn. Sem. LOMI 30 (1972), 33-40 (in Russian) 
  6. [6] J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves Clarendon Press, Oxford, 1996 
  7. [7] M. Putinar, The superposition property for Taylor's functional calculus J. Operator Theory 7 (1982), 149-155 Zbl0483.46028
  8. [8] S. Sandberg, On non-holomorphic functional calculus for commuting operatorspreprint, 1999 Zbl0929.47008
  9. [9] J. L. Taylor, A joint spectrum for several commuting operators J. Funct. Anal. 6 (1970), 172-191 Zbl0233.47024
  10. [10] J. L. Taylor, The analytic-functional calculus for several commuting operators Acta Math. 125 (1970), 1-38 Zbl0233.47025
  11. [11] J. L. Taylor, Homology and cohomology for topological algebras Adv. Math. 9 (1972), 137-182 Zbl0271.46040
  12. [12] J. L. Taylor, A general framework for a multi-operator functional calculus ibid., 184-252 

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