Search results for "Homomorphism"
showing 8 items of 28 documents
Regularity and Algebras of Analytic Functions in Infinite Dimensions
1996
A Banach space E E is known to be Arens regular if every continuous linear mapping from E E to E ′ E’ is weakly compact. Let U U be an open subset of E E , and let H b ( U ) H_b(U) denote the algebra of analytic functions on U U which are bounded on bounded subsets of U U lying at a positive distance from the boundary of U . U. We endow H b ( U ) H_b(U) with the usual Fréchet topology. M b ( U ) M_b(U) denotes the set of continuous homomorphisms ϕ : H b ( U ) → C \phi :H_b(U) \to \mathbb {C} . We study the relation between the Arens regularity of the space E E and the structure of M b ( U ) M_b(U) .
Homomorphisms between Algebras of Holomorphic Functions
2014
For two complex Banach spaces X and Y, in this paper, we study the generalized spectrum M-b(X,Y) of all nonzero algebra homomorphisms from H-b(X), the algebra of all bounded type entire functions on X into H-b(Y). We endow M-b(X,Y) with a structure of Riemann domain over L(X*,Y*) whenever.. is symmetrically regular. The size of the fibers is also studied. Following the philosophy of ( Aron et al., 1991), this is a step to study the set M-b,M-infinity (X,B-Y) of all nonzero algebra homomorphisms from Hb(b) (X) into H-infinity (B-Y) of bounded holomorphic functions on the open unit ball of Y and M-infinity(B-X,B-Y) of all nonzero algebra homomorphisms from H-infinity(B-X) into H infinity (B-Y…
Chern classes of the moduli stack of curves
2005
Here we calculate the Chern classes of ${\bar {\mathcal M}}_{g,n}$, the moduli stack of stable n-pointed curves. In particular, we prove that such classes lie in the tautological ring.
Equivariant cohomology, Fock space and loop groups
2006
Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.
On the Existence and Structure of Ψ*-Algebras of Totally Characteristic Operators on Compact Manifolds with Boundary
1999
As a contribution to the pseudodifferential analysis on manifolds with singularities we construct for each smooth, compact manifold X with boundary a Ψ*-algebra A(b)∞(X, bΩ1/2)⊆L(ϱbL2(X, bΩ1/2)) containing the algebra Ψ0b, cl(X, bΩ1/2) of totally characteristic pseudodifferential operators introduced by Melrose [25] in 1981 as a dense subalgebra; further, there is a homomorphism τ(b)A: A(b)∞(X, bΩ1/2)→Q(b)Ψ characterizing the Fredholm property of a∈A(b)∞(X, bΩ1/2) by means of the invertibility of τ(b)A(a)∈Q(b)Ψ, where Q(b)Ψ is an algebra of C∞-symbols reflecting the smooth structure of the manifold X. The Fredholm inverses of Fredholm operators in A(b)∞(X, bΩ1/2) are again in the algebra A(…
Holomorphic de Rham Cohomology
2017
We are going to define a natural comparison isomorphism between algebraic de Rham cohomology and singular cohomology of varieties over the complex numbers with coefficients in \(\mathbb {C}\). The link is provided by holomorphic de Rham cohomology, which we study in this chapter.
Are images in the Tractatus isomorphic to facts?
2010
The notion of image (Bild) is a fundamental one in the Tractatus. This notion is immediately introduced in the text after the brief ontological section, because it serves to give an account in logical terms of our relationship with the world. The relationship between fact and image is generally considered a relationship governed by a form of isomorphism. Here I want to maintain that it is not a matter isomorphism, but instead of homomorphism.
About Vertex Mappings
2019
Summary In [6] partial graph mappings were formalized in the Mizar system [3]. Such mappings map some vertices and edges of a graph to another while preserving adjacency. While this general approach is appropriate for the general form of (multidi)graphs as introduced in [7], a more specialized version for graphs without parallel edges seems convenient. As such, partial vertex mappings preserving adjacency between the mapped verticed are formalized here.