We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented maps by a class of K-oriented normal maps, which are maps together with a certain factorisation. Our construction does not use any special features of equivaria...

We investigate the problem of type isomorphisms in the presence of higherorder references. We first introduce a finitary programming language with sum types and higher-order references, for which we build a fully abstract games model following the work of Abramsky, Honda and McCusker. Solving an open problem by Laurent, we show that two finitely branching arenas are isomorphic if and only if th...

In this paper, we investigate the role of square functions defined for a d-tuple commuting Ritt operators $$(T_1,\ldots ,T_d)$$ acting on general Banach space X. Firstly, prove that if admits $$H^\infty $$ joint functional calculus, then it verifies various function estimates. Then study converse when every $$T_k$$ is R-Ritt operator. Under last hypothesis, and X K-convex space, show estimates ...

For graphs G and G' with minimum degree is = 3 and satisfying one of two other conditions, we prove that any isomorphism from the P4 -graph P4 (G) to P4 ( G') can be induced by a vertex-isomorphism of G onto G'. We also prove that a connected graph G is isomorphic to its P4 -graph P4 (G) if and only if G is a cycle of length at least 4.