On uniqueness of distribution of a random variable whose independent copies span a subspace in $L_{p}$

• Autorzy: S. Astashkin , F. Sukochev , D. Zanin
• Języki publikacji: EN

Abstrakty

EN

Let 1 ≤ p < 2 and let $L_{p}= L_{p}[0,1]$ be the classical $L_{p}$-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable $f ∈ L_{p}$ spans in $L_{p}$ a subspace isomorphic to some Orlicz sequence space $l_{M}$. We give precise connections between M and f and establish conditions under which the distribution of a random variable $f ∈ L_{p}$ whose independent copies span $l_{M}$ in $L_{p}$ is essentially unique.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 230
• Numer: 1
• Strony: 41-57

Daty

wydano

2015

Twórcy

autor

S. Astashkin

• Samara State University, Pavlova 1, 443011, Samara, Russia
• Samara State Aerospace University (SSAU), Moskovskoye shosse 34, 443086, Samara, Russia

autor

F. Sukochev

• School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia

autor

D. Zanin

• School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia

Identyfikatory

DOI

10.4064/sm8089-1-2016