Using a technique of B. Maurey which he has proposed for the proof of the famous Enflo theorem on primarity of the space $L_p$, we introduce and investigate a notion of Maurey measure for arbitrary continuous linear operator acting on $L_p$ and a notion of Maurey operator. The last notion can be considered as a generalization of the notion of compact operator on $L_p$ -spaces. The main result asserts that every operator which is not a Maurey operator is an isomorphic embedding on some subspace isomorphic to $L_p$. Since the set of all Maurey operators is a subspace of the space of all continuous linear maps not containing the identity, this result can be considered as a generalization of Enflo's theorem on primarity.
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- ACS Style
- Krasikova, I.V.; Popov, M.M. On a generalization of the concept of a compact operator on spaces $L_p$. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Krasikova IV, Popov MM. On a generalization of the concept of a compact operator on spaces $L_p$. Bukovinian Mathematical Journal. 2018; 1(501).
- Chicago/Turabian Style
- Iryna Volodymyrivna Krasikova, Mykhailo Mykhailovych Popov. 2018. "On a generalization of the concept of a compact operator on spaces $L_p$". Bukovinian Mathematical Journal. 1 no. 501.