2 00 1 Crossed products of C ( X ) - algebras by endomorphisms and C ( X ) - categories . ( Preliminary Draft )
نویسنده
چکیده
We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that it becomes induced by a Hilbert C(X)-bimodule. Furthermore we introduce the notion of C(X)-category, and discuss relationships with crossed products and duality for compact groups.
منابع مشابه
2 00 3 Ideal Structure of C ∗ - Algebras Associated with C ∗ - Correspondences
We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...
متن کاملIdeal Structure of C * -algebras Associated with C * -correspondences
We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...
متن کاملar X iv : 0 70 8 . 42 79 v 2 [ m at h . K T ] 2 9 M ay 2 00 8 A LEFSCHETZ FIXED - POINT FORMULA FOR CERTAIN ORBIFOLD C * - ALGEBRAS
Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product C-algebras C0(X)⋊ G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊ G induced by the endomorphism, i.e. the Lefschetz n...
متن کاملQuasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...
متن کاملCrossed Products by Semigroups of Endomorphisms and the Toeplitz Algebras of Ordered Groups
Let I+ be the positive cone in a totally ordered abelian group F. We construct crossed products by actions of J+ as endomorphisms of C*algebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C*-algebras generated by two semigroups V, W: I+ -+ B(H) of nonunitary isometrics are canonically isomorphic, thus giving a new, sel...
متن کامل