Abstract

In (1966), T. West \cite{Wes} showed that if $X$ is a Hilbert space, then every Riesz operator $R$ can be written under the form $R = K + Q$ where $K$ is a compact operator and $Q$ is quasinilpotent (its spectrum is reduced to the set $\{0\}$), twenty years after, K. Davidson and D. Herrero (1986) proved this decomposition for such operators on $l_p (1 \leq p < \infty)$ spaces and $c_0$ or more generally on the spaces having the finite dimensional p-Block decomposition (FDPBD) written as an infinite direct sum of finite dimensional spaces. In (1988), H. Zhong \cite{Zho3} gave an affirmative answer to this problem if $X = L_p(\mu)$ $(1 < p < \infty)$ and extended his results to the case of B-convex Banach space. Finally in (1995), the last author showed that the result holds for the case of local strong subprojective Banach spaces, in particular, he studies it's validity in the case of Tsirelson space. Since every Banach space $X$ has a type $p(X) \in [1, 2]$ and the fact that $1<p(X)$ is equivalent to the fact that $X$ is a B-convex Banach space implies the necessity to investigate the West decomposition of Riesz operators on Banach spaces with type 1.

Information

Item Type:	Journal
Divisions:	» Laboratory of Computer Science and Mathematics
ePrint ID:	917
Date Deposited:	2017-10-01
Further Information:	Google Scholar
URI:	https://www.univ-soukahras.dz/en/publication/article/917

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