R c(x)dx = 1. For any sufficiently large number K the space Lp([−K,K]) of all Lp-functions with support in the interval [−K,K] is an invariant space of Wc,α. It is known that Wc,α restricted to Lp([−K,K]) is a compact operator with eigenvalues α−k, k = 0, 1, . . . , and spectrum {α−k : k = 1, 2, . . .} ∪ {0}, which are independent of c and K. This result is better understood in the context of w...

Nowak [N], improving a theorem due to A. N. Dranishnikov, G. Gong, V. Lafforgue, and G. Yu [DGLY], gave a characterization of coarse embeddability of general metric spaces into a Hilbert space using a result of Schoenberg on negative definite kernels. He used this characterization to show that the spaces Lp(μ) coarsely embed into a Hilbert space for p < 2. In this article, we show that lp does ...

December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...

Lumboperitoneal (LP) and ventriculoperitoneal (VP) shunts are a frequent treatment modality for idiopathic intracranial hypertension (IIH). Although these shunts have been used for a long time, it is still not clear how they change the total craniospinal CSF volume and what portions of cranial and spinal CSF are affected. This report for the first time presents the results of a volumetric analy...

In this paper we consider unbounded weighted conditional type (WCT) operators on Lp-space. We provide some conditions under which WCT Lp-spaces are densely defined. Specifically, obtain a dense subset of their domain. Moreover, get that operator is continuous if and only it every where A description polar decomposition, spectrum, spectral radius, normality hyponormality in context provided. Fin...

We show that a separable proximinal subspace of X, say Y is strongly proximinal (strongly ball proximinal) if and only if Lp(I, Y ) is strongly proximinal (strongly ball proximinal) in Lp(I,X), for 1 ≤ p <∞. The p =∞ case requires a stronger assumption, that of ’uniform proximinality’. Further, we show that a separable subspace Y is ball proximinal in X if and only if Lp(I, Y ) is ball proximin...

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of Lp-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any Lp-space into any Banach space X containing the l n p ’s. Finally using an...

As p—► » we get the space E„ with the distance function max,-=i,... ,m | x< — as/ |. Let, furthermore, lp stand for the space of real sequences with the series of pth powers of the absolute values convergent. Similarly let Lp denote the space of real measurable functions in the interval (0, 1) which are oummable to the ^»th power, while C shall mean the space of real continuous functions in the...

Let f=∑k=0∞ckh2k, where {hn} is the classical Haar system, ck∈ℂ. Given a p∈(1,∞), we find sharp conditions, under which sequence {fn}n=1∞ of dilations and translations f basis in space Lp[0,1], equivalent to {hn}n=1∞. The results obtained depend substantially on whether p≥2 or 1<p<2 include as endpoints Lp-scale spaces BMOd Hd1. proofs are based an appropriate splitting set positive integers N=...