In the paper we consider T1, . . . , Td absolute contractions of von Neumann algebra M with normal, semi-finite, faithful trace, and prove that for every bounded Besicovitch weight {a(k)} k∈Nd and every x ∈ Lp(M), (p > 1) the averages

Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of lp distance measures, researchers were motivated to use them in almost every clustering process. Beside lp distance measures, there exist several distance measures. Sargent introduced a special type of distance measuresm(φ) and n(φ) which is closely r...

We show that the Hilbert space is coarsely embeddable into any lp for 1 ≤ p < ∞. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space. Coarse embeddings were defined by M. Gromov [Gr] to express the idea of inclusion in the large scale geometry of groups. G. Yu showed later that the case when a finitely generated group with a word l...