• Korean Journal of Mathematics
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• 제30권1호
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• pp.147-154
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• 2022

In this article, we prove that an absolutely summing operator on 𝓛^λ₁ spaces has a lifting under the conditions that a target Banach space is a quotient of reflexive Banach subspaces.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.645-655
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• 2019

In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given $Pelcz{\acute{y}}nski$ theorem for complemented subspaces of ${\ell}_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1({\mu})$.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.447-456
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• 2015

In this paper we show that some operators defined on the Banach space with an unconditional basis and $L^1({\mu})$ into a Banach space with the RNP have liftable operators.

• 대한수학회논문집
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• 제16권1호
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• pp.119-124
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• 2001

In the paper we show that some operators defined on L$^1$($\mu$) and on C(K) into Banach space with the RNP have the lifting property.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.385-389
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• 2023

In this article, we prove that an infinite dimensional complemented subspace X of 𝓛₁-space Z with unconditional basis (x_n) has the lifting property. Hence we can give an alternative proof that X is isomorphic to ℓ₁ given by Lindenstrauss and Pelczyński.

• 대한수학회지
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• 제46권6호
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• pp.1293-1307
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• 2009

We give conditions so that a polynomial be factorable through an $L_{\gamma}({\mu})$ space. Among them, we prove that, given a Banach space X and an index m, every absolutely summing operator on X is 1-factorable if and only if every 1-dominated m-homogeneous polynomial on X is right 1-factorable, if and only if every 1-dominated m-homogeneous polynomial on X is left 1-factorable. As a consequence, if X has local unconditional structure, then every 1-dominated homogeneous polynomial on X is right and left 1-factorable.