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Strictly Singular and Cosingular Multiplications

  • Mikael Lindström (a1), Eero Saksman (a2) and Hans-Olav Tylli (a3)

Abstract

Let $L(X)$ be the space of bounded linear operators on the Banach space $X$ . We study the strict singularity and cosingularity of the two-sided multiplication operators $S\,\mapsto \,ASB$ on $L(X)$ , where $A,\,B\,\in \,L(X)$ are fixed bounded operators and $X$ is a classical Banach space. Let $1\,<\,p\,<\,\infty $ and $p\,\ne \,2$ . Our main result establishes that the multiplication $S\,\mapsto \,ASB$ is strictly singular on $L\left( {{L}^{p}}\left( 0,\,1 \right) \right)$ if and only if the non-zero operators $A,\,B\,\in \,L\left( {{L}^{p}}\left( 0,\,1 \right) \right)$ are strictly singular. We also discuss the case where $X$ is a ${\mathcal{L}^{1}}-$ or a ${{\mathcal{L}}^{\infty }}-$ space, as well as several other relevant examples.

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References

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Strictly Singular and Cosingular Multiplications

  • Mikael Lindström (a1), Eero Saksman (a2) and Hans-Olav Tylli (a3)

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