SMALL SUBSPACES OF Lp

A New Class of Banach Sequence Spaces

SPECTRAL SUBSPACES OF L p FOR p < 1

Let Ω be an open subset of Rn. Denote by LpΩ(R n) the closure in Lp(Rn) of the set of all functions ε ∈ L1(Rn)∩Lp(Rn) whose Fourier transform has compact support contained in Ω. The subspaces of the form LpΩ(R n) are called the spectral subspaces of Lp(Rn). It is easily seen that each spectral subspace is translation invariant; i.e., f(x + a) ∈ LpΩ(R) for all f ∈ L p Ω(R n) and a ∈ Rn. Sufficie...

ar X iv : m at h / 03 07 16 9 v 1 [ m at h . FA ] 1 1 Ju l 2 00 3 On Subspaces of Non - commutative L p - Spaces

We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non necessarily semi-finite) von Neumann algebra a. If a subspace X of Lp(a) contains uniformly the spaces lnp , n ≥ 1, it contains an almost isometric, almost 1-complemented copy of lp. If X contains uniformly the finite dimensional Schatten classes S p , it contains their l...

lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

Abstract: We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric outliers. We study the recovery of the global l0 subspace (i.e., with largest number of points) by minimizing the lp-averaged distances of data points from d-dimensional subspaces of R , where 0 < p ∈ R. Unlike other lp minimization problems, this minimization is non-convex for all p > 0...

SUBSPACES OF Lp THAT EMBED INTO Lp(μ) WITH μ FINITE

Enflo and Rosenthal [4] proved that `p(א1), 1 < p < 2, does not (isomorphically) embed into Lp(μ) with μ a finite measure. We prove that if X is a subspace of an Lp space, 1 < p < 2, and `p(א1) does not embed into X, then X embeds into Lp(μ) for some finite measure μ.