Narrow and ℓ2-strictly singular operators from L p
Copyright policy )Narrow and ℓ2-strictly singular operators from L p
In the first part of the paper we prove that for $2 < p, r < \infty$ every operator $T: L_p \to \ell_r$ is narrow. This completes the list of sequence and function Lebesgue spaces $X$ with the property that every operator $T:L_p \to X$ is narrow. Next, using similar methods we prove that every $\ell_2$-strictly singular operator from $L_p$, $1
Dedicated to the memory of Joram Lindenstrauss
- Miami University United States
- Chernivtsi National University Ukraine
- Weizmann Institute of Science Israel
Banach lattices, Primary 47B07, secondary 47B38, 46B03, 46E30, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, sign-embedding, Linear operators on function spaces (general), Linear operators defined by compactness properties, FOS: Mathematics, narrow operator, Classical Banach spaces in the general theory
Banach lattices, Primary 47B07, secondary 47B38, 46B03, 46E30, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, sign-embedding, Linear operators on function spaces (general), Linear operators defined by compactness properties, FOS: Mathematics, narrow operator, Classical Banach spaces in the general theory
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