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 5 → ASB on L(X), where A, B ∈ L(X) are fixed bounded operators and X is a classical Banach space. Let 1 < p < ∞ and p ≠ 2. Our main result establishes that the multiplication S → ASB is strictly singular on L(Lp(0, 1)) if and only if the non-zero operators A, B ∈ L(Lp(0,1)) are strictly singular. We also discuss the case where X is a ℒ1 - or a ℒ ∞-space, as well as several other relevant examples. ©Canadian Mathematical Society 2005.
Original language | English |
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Pages (from-to) | 1249-1278 |
Number of pages | 30 |
Journal | Canadian Journal of Mathematics |
Volume | 57 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2005 |
MoE publication type | A1 Journal article-refereed |