The Kadec-Pelczynski theorem in Lp, 1 ≤ p ≤ 2

I. Berkes; R. Tichy

doi:10.1090/proc/12872

The Kadec-Pelczynski theorem in L^p, 1 ≤ p ≤ 2

I. Berkes
, R. Tichy

Research output: Contribution to journal › Article › peer-review

Abstract

By a classical result of Kadec and Pelczynski (1962), every normalized weakly null sequence in L^p, p > 2 contains a subsequence equivalent to the unit vector basis of ℓ² or to the unit vector basis of ℓ^p. In this paper we investigate the case 1 ≤ p < 2 and show that a necessary and sufficient condition for the first alternative in the Kadec-Pelczynski theorem is that the limit random measure μ of the sequence satisfies ∫_ℝ x²dμ(x) ∈ L^p/2.

Original language	English
Pages (from-to)	2053-2066
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	5
DOIs	https://doi.org/10.1090/proc/12872
Publication status	Published - 2016

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

Access to Document

10.1090/proc/12872

S0002-9939-2015-12872-9Final published version, 251 KBLicence: CC BY 4.0

Cite this

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title = "The Kadec-Pelczynski theorem in Lp, 1 ≤ p ≤ 2",

abstract = "By a classical result of Kadec and Pelczynski (1962), every normalized weakly null sequence in Lp, p > 2 contains a subsequence equivalent to the unit vector basis of ℓ2 or to the unit vector basis of ℓp. In this paper we investigate the case 1 ≤ p < 2 and show that a necessary and sufficient condition for the first alternative in the Kadec-Pelczynski theorem is that the limit random measure μ of the sequence satisfies ∫ℝ x2dμ(x) ∈ Lp/2. ",

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AU - Tichy, R.

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N2 - By a classical result of Kadec and Pelczynski (1962), every normalized weakly null sequence in Lp, p > 2 contains a subsequence equivalent to the unit vector basis of ℓ2 or to the unit vector basis of ℓp. In this paper we investigate the case 1 ≤ p < 2 and show that a necessary and sufficient condition for the first alternative in the Kadec-Pelczynski theorem is that the limit random measure μ of the sequence satisfies ∫ℝ x2dμ(x) ∈ Lp/2.

AB - By a classical result of Kadec and Pelczynski (1962), every normalized weakly null sequence in Lp, p > 2 contains a subsequence equivalent to the unit vector basis of ℓ2 or to the unit vector basis of ℓp. In this paper we investigate the case 1 ≤ p < 2 and show that a necessary and sufficient condition for the first alternative in the Kadec-Pelczynski theorem is that the limit random measure μ of the sequence satisfies ∫ℝ x2dμ(x) ∈ Lp/2.

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DO - 10.1090/proc/12872

M3 - Article

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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The Kadec-Pelczynski theorem in Lp, 1 ≤ p ≤ 2