Uniform embeddings of bounded geometry spaces into reflexive Banach space
By N. Brown, E. Guentner. 2003
49 citations recorded by the source corpus.
We show that every metric space with bounded geometry uniformly embeds into a direct sum of l p (N) spaces (p's going off to infinity). In particular, every sequence of expanding graphs uniformly embeds into such a reflexive Banach space even though no such sequence uniformly embeds into a fixed l p (N) space. In the case of discrete groups we prove the analogue of a-T-menability - the existence of a metrically proper affine isometric action on a direct sum of l p (N) spaces.
View Paper: https://www.semanticscholar.org/paper/2cbc72765e51337dd69b6ba4968dac8c2ea95bde
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Citations in the corpus
- Property (T) and rigidity for actions on Banach spaces (2005, background): “‡ For spaces that are only strictly convex, the fixed point property always fails [ BG ],[HP].”
- Isometric Group Actions on Banach Spaces and Representations Vanishing at Infinity (2006, background): “† (U. Haagerup and A. Przybyszewska [HP], generalizing a previous result in [ BG ]) Every separable locally compact group G admits a proper isometric action on the strictly convex Banach space ' 1 n=1L 2n (G), where ' denotes”
- The coarse geometric Novikov conjecture and uniform convexity (2005, background): “strictly convex and reflexive Banach space [ 3 ] (recall that a Banach space X is said to be strictly convex if x+y 2 < 1 for any two distinct unit vectors x and”
- The Novikov conjecture and geometry of Banach spaces (2012, background): “By the above theorems, a positive answer to this question would imply the Novikov conjecture since every countable group admits a coarse embedding into C0 (see Brown and Guentner [4]).”
- The non-linear geometry of Banach spaces after Nigel Kalton (2012, background): “Any metric space with bounded geometry coarsely embeds into a reflexive space [17].”
- Some notes on Property A (2006, background): “[ BG05 ] proves that any bounded geometry space coarsely embeds into a reflexive, strictly convex Banach space.”