Shift-invariant functionals on Banach sequence spaces

Albrecht Pietsch

Studia Mathematica, Tome 215 (2013), p. 37-66 / Harvested from The Polish Digital Mathematics Library

Résumé

The present paper is a continuation of [23], from which we know that the theory of traces on the Marcinkiewicz operator ideal $(H) : = T \in (H) : s u p_{1 \leq m < \infty} 1 / (l o g m + 1) \sum_{n = 1}^{m} a ₙ (T) < \infty$ can be reduced to the theory of shift-invariant functionals on the Banach sequence space $(ℕ ₀) : = c = (γ_{l}) : s u p_{0 \leq k < \infty} 1 / (k + 1) \sum_{l = 0}^{k} | γ_{l} | < \infty$ . The final purpose of my studies, which will be finished in [24], is the following. Using the density character as a measure, I want to determine the size of some subspaces of the dual *(H). Of particular interest are the sets formed by the Dixmier traces and the Connes-Dixmier traces (see [2], [4], [6], and [13]). As an intermediate step, the corresponding subspaces of *(ℕ₀) are treated. This approach has a significant advantage, since non-commutative problems turn into commutative ones.

Publié le : 2013-01-01

Zbl 1280.46012

EUDML-ID : urn:eudml:doc:285899

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     title = {Shift-invariant functionals on Banach sequence spaces},
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     volume = {215},
     year = {2013},
     pages = {37-66},
     zbl = {1280.46012},
     language = {en},
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Albrecht Pietsch. Shift-invariant functionals on Banach sequence spaces. Studia Mathematica, Tome 215 (2013) pp. 37-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-3/