Shift-invariant functionals on Banach sequence spaces

Albrecht Pietsch. "Shift-invariant functionals on Banach sequence spaces." Studia Mathematica 214.1 (2013): 37-66. <http://eudml.org/doc/285899>.

@article{AlbrechtPietsch2013,
abstract = {The present paper is a continuation of [23], from which we know that the theory of traces on the Marcinkiewicz operator ideal $ (H):= \{T ∈ (H): sup_\{1≤m<∞\} 1/(log m + 1) ∑_\{n=1\}^\{m\} aₙ(T) < ∞\}$ can be reduced to the theory of shift-invariant functionals on the Banach sequence space $(ℕ₀):= \{c = (γ_\{l\}): sup_\{0≤k<∞\} 1/(k+1) ∑_\{l=0\}^\{k\} |γ_\{l\}| < ∞\}$. 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.},
author = {Albrecht Pietsch},
journal = {Studia Mathematica},
keywords = {shift-invariant functional; Banach sequence space; trace; operator ideal; medium-sized subspace},
language = {eng},
number = {1},
pages = {37-66},
title = {Shift-invariant functionals on Banach sequence spaces},
url = {http://eudml.org/doc/285899},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Albrecht Pietsch
TI - Shift-invariant functionals on Banach sequence spaces
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 1
SP - 37
EP - 66
AB - The present paper is a continuation of [23], from which we know that the theory of traces on the Marcinkiewicz operator ideal $ (H):= {T ∈ (H): sup_{1≤m<∞} 1/(log m + 1) ∑_{n=1}^{m} aₙ(T) < ∞}$ can be reduced to the theory of shift-invariant functionals on the Banach sequence space $(ℕ₀):= {c = (γ_{l}): sup_{0≤k<∞} 1/(k+1) ∑_{l=0}^{k} |γ_{l}| < ∞}$. 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.
LA - eng
KW - shift-invariant functional; Banach sequence space; trace; operator ideal; medium-sized subspace
UR - http://eudml.org/doc/285899
ER -