Geodesic
A note on a paper by Piszczek on Jordan decomposition in noncommutative Schwartz space
Subhash J. Bhatt1
1 Department of Mathematics Sardar Patel University Vallabh Vidyanagar, Gujarat 388120, India
Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 225-230.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The positive cone in a closed $^*$-subalgebra of the noncommutative Schwartz algebra of smooth operators is normal, which immediately implies decomposition of a continuous self-adjoint functional as a difference of two positive functionals. A~decomposition as a difference of two representable positive functionals holds precisely for self-adjoint functionals continuous in the $C^*$-operator norm.
DOI : 10.4064/cm6922-6-2016
Keywords: positive cone closed * subalgebra noncommutative schwartz algebra smooth operators normal which immediately implies decomposition continuous self adjoint functional difference positive functionals decomposition difference representable positive functionals holds precisely self adjoint functionals continuous * operator norm

Subhash J. Bhatt 1

1 Department of Mathematics Sardar Patel University Vallabh Vidyanagar, Gujarat 388120, India 
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Subhash J. Bhatt. A note on a paper by Piszczek on Jordan decomposition in noncommutative Schwartz space. Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 225-230. doi : 10.4064/cm6922-6-2016. http://geodesic.mathdoc.fr/articles/10.4064/cm6922-6-2016/

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