EMBEDDING FUNCTION SPACES INTO `∞/c0
نویسنده
چکیده
We show that if the space `∞/c0 contains an isometric copy of every function space over a first countable compactum or every function space over a Corson copactum of weight not exceeding the continuum then every subset of R belongs to the σfield generated by sets of the form A1×A2.We prove a similar result about isomorphic rather than isometric embeddings into `∞/c0 in terms of the σ-field of subsets of R generated by sets of the form A1 × · · · ×Ak for other positive integers k.
منابع مشابه
A Metric Space Not Quasi-isometrically Embeddable into Any Uniformly Convex Banach Space
We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...
متن کاملRemarks on Quasi-isometric Non-embeddability into Uniformly Convex Banach Spaces
We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...
متن کاملComplementably Universal Banach Spaces, Ii
The two main results are: A. If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X∗ is non separable (and hence X does not embed into c0), B. There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X. Theorem B solves a problem that dates from the 1970s.
متن کاملar X iv : 1 61 1 . 01 35 5 v 1 [ m at h . FA ] 4 N ov 2 01 6 Disjointness preserving C 0 - semigroups and local operators on ordered Banach spaces
We generalize results concerning C0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local C0-semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norm...
متن کاملSmooth functions on c0
The space c0 lies at the heart of many constructions of higher order smooth functions on Banach spaces. To name a few, recall Torunczyk’s proof of the existence of C-smooth partitions of unity on WCG spaces ([12]) or Haydon’s recent constructions of C-bump functions on certain C(K) spaces ([7]). The crucial property of c0 that allows for those constructions is a rich supply of C -smooth functio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010