In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

The Yoneda Lemma tells us that the Hom bifunctor is “non-degenerate” in a similar way. (a) For each object X ∈ C verify that hX := HomC(X,−) defines a functor C → Set. (b) Given two objects X,Y ∈ C state what it means to have hX ≈ hY as functors. (c) Given two objects X,Y ∈ C and an isomorphism of functors hX ≈ hY , prove that we have an isomorphism of objects X ≈ Y . [Hint: Let Φ : hX ∼ −→ hY ...

We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in analysis such as isomorphism of C∗-algebras and affine homeomorphism of Choquet simplices, where among other things we provide a simple proof of the completeness ...

We prove that the isomorphism relation for separable C∗-algebras, and also the relations of complete and n-isometry for operator spaces and systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a standard Borel space.

The group isomorphism problem consists in deciding whether two groups G and H given by their multiplication tables are isomorphic. An algorithm for group isomorphism attributed to Tarjan runs in time n, c.f. [Mil78]. Miller and Monk showed in [Mil79] that group isomorphism can be many-one reduced to isomorphism testing for directed graphs. For groups with n elements, the graphs have valence at ...

For an orbifold X and α ∈ H(X,Z), we introduce the twisted cohomologyH c (X, α) and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups K α (X)⊗C and twisted cohomologyH c (X, α). This theorem, on the one hand, generalizes a classical result of Baum-Connes, Brylinski-Nistor, and others, that if X is an orbifold then the Chern character establishes an is...

We exploit the Fedosov-Weinstein-Xu (FWX) resolution proposed in q-alg/9709043 to establish an isomorphism between the ring of Hochschild cohomology of the quantum algebra of functions on a symplectic manifold M and the ring H(M,C((~))) of De Rham cohomology of M with the coefficient field C((~)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket ...