Abstract
During half a century, singular traces on ideals of Hilbert space operators have been constructed by looking for linear forms on associated sequence ideals. Only recently, the author was able to eliminate this auxiliary step by directly applying Banach’s version of the extension theorem; see (Integral Equ. Oper. Theory 91, 21, 2019 and 92, 7, 2020). Of course, the relationship between the new approach and the older ones must be investigated. In the first paper, this was done for \({\mathfrak {L}}_{1,\infty } (H)\). To save space, such considerations were postponed in the second paper, which deals with a large class of principal ideals, called simply generated. This omission will now be rectified.
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References
Banach, S.: Théorie des opérations linéaires. Warszawa (1932)
Levitina, G., Usachev, A.: Traces on principal ideals, preprint
Lord, S., Sukochev, F., Zanin, D.: Singular Traces. De Gruyter, Berlin (2013)
Pietsch, A.: A new approach to operator ideals on Hilbert space and their traces. Integral Equ. Oper. Theory 89, 595–606 (2017)
Pietsch, A.: A new view at Dixmier traces on \({\mathfrak{L}}_{1,\infty } (H)\). Integral Equ. Oper. Theory 91, 21 (2019)
Pietsch, A.: The existence of singular traces on simply generated operator ideals. Integral Equ. Oper. Theory 92, 7 (2020)
Sucheston, L.: Banach limits. Am. Math. Mon. 74, 308–311 (1967)
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Pietsch, A. More about singular traces on simply generated operator ideals. Arch. Math. 115, 299–308 (2020). https://doi.org/10.1007/s00013-020-01475-y
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DOI: https://doi.org/10.1007/s00013-020-01475-y