Representations of Banach algebras as algebras of completely bounded maps

DOI10.7146/MATH.SCAND.A-15108zbMATH Open1187.46037arXiv1009.4278OpenAlexW197611855MaRDI QIDQ3396180

T. Oikhberg

Publication date: 16 September 2009

Published in: MATHEMATICA SCANDINAVICA (Search for Journal in Brave)

Abstract: For an operator $TinB(X,Y)$, we denote by $a_m(T)$, $c_m(T)$, $d_m(T)$, and $t_m(T)$ its approximation, Gelfand, Kolmogorov, and absolute numbers. We show that, for any infinite dimensional Banach spaces $X$ and $Y$, and any sequence $alph{a}_{m}searrow0$, there exists $TinB(X,Y)$ for which the inequality ${\displaystyle }$ 3 alpha_{lceil m/6 ceil} geq a_m(T) geq max{c_m(t), d_m(T)} geq min{c_m(t), d_m(T)} geq t_m(T) geq alpha_m/9 ${\displaystyle }$ holds for every $minN$. Similar results are obtained for other $s$-scales.

Full work available at URL: https://arxiv.org/abs/1009.4278

zbMATH Keywords

operator spaces\(2\)-summing operatorsrepresentation of Banach algebras

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Operator spaces (= matricially normed spaces) (47L25) Representations of topological algebras (46H15) Operator ideals (47L20) Algebras of operators on Banach spaces and other topological linear spaces (47L10)

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