On Enflo and narrow operators acting on L_p

2012/01/19 by Mykhaylyuk, V., Popov, M., Randrianantoanina, B.
#46B03 (Secondary) #47B07 (Primary) 47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1201.4041

Abstract

The first part of the paper is inspired by a theorem of H. Rosenthal, that if an operator on L₁[0,1] satisfies the assumption that for each measurable set A ⊆ [0,1] the restriction T |_L1(A) is not an isomorphic embedding, then the operator is narrow. (Here L₁(A) = \x ∈ L₁: \rm supp x ⊆ A \.) This leads to a natural question of finding mildest possible assumptions for operators on a given space X, which will imply that the operator is narrow. We find a partial answer to this question for operators on L_p(0,1) with 1

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