Articles

Copies of ℓ ₁ in positive tensor products of Orlicz sequence spaces

Published in: Quaestiones Mathematicae
Volume 34 , issue 4 , 2011 , pages: 407–415

DOI: 10.2989/16073606.2011.640431

Author(s): Qingying Bu* Department of Mathematics, USA , Donghai Ji Department of Mathematics, China , Yongjin Li† Department of Mathematics, China

Keywords: 46B42 , 46B28 , 46B42 , 46B28

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Abstract

Let X be a Banach lattice and ℓ _ϕ be an Orlicz sequence space associated to an Orlicz function ϕ with the Δ₂-condition. In this paper, we prove that (i) the positive injective tensor product of ℓ _ϕ and X, contains no copy of ℓ₁ if and only if both ℓ _ϕ and X contain no copy of ℓ ₁; and (ii) the positive projective tensor product of ℓ _ϕ and X, contains no copy of ℓ ₁ if and only if both ℓ _ϕ and X contain no copy of ℓ ₁ and each positive linear operator from ℓ _ϕ to X* is compact.

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