The regularity of Dunford-Pettis operators

Holub, James R.

doi:10.1090/S0002-9939-1988-0958049-0

The regularity of Dunford-Pettis operators
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Proc. Amer. Math. Soc. 104 (1988), 89-95 Request permission

Abstract:

Let $\lambda$ denote a symmetric, solid Banach sequence space having $\left \{ {{e_i}} \right \}_{i = 1}^\infty$ as a symmetric basis and considered as a Banach lattice with order defined coordinatewise. A complete description of the relationship between regular and Dunford-Pettis operators $T:{L^1}[0,1] \to \lambda$ is given. The results obtained complete earlier work of Gretsky and Ostroy and of the author in this area.

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