6,583 research outputs found
The Gelfand map and symmetric products
If A is an algebra of functions on X, there are many cases when X can be
regarded as included in Hom(A,C) as the set of ring homomorphisms. In this
paper the corresponding results for the symmetric products of X are introduced.
It is shown that the symmetric product Sym^n(X) is included in Hom(A,C) as the
set of those functions that satisfy equations generalising f(xy)=f(x)f(y).
These equations are related to formulae introduced by Frobenius and, for the
relevant A, they characterise linear maps on A that are the sum of ring
homomorphisms. The main theorem is proved using an identity satisfied by
partitions of finite sets.Comment: 14 pages, Late
Approximate Homomorphisms of Ternary Semigroups
A mapping between ternary semigroups will be
called a ternary homomorphism if . In this paper,
we prove the generalized Hyers--Ulam--Rassias stability of mappings of
commutative semigroups into Banach spaces. In addition, we establish the
superstability of ternary homomorphisms into Banach algebras endowed with
multiplicative norms.Comment: 10 page
Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem
(Write-up of a talk at the Bialowieza meeting, July 2007.)
Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological
space can be canonically embedded into the infinite-dimensional vector
space , the dual space of the algebra of continuous functions
as an "algebraic variety" specified by an infinite system of quadratic
equations.
Buchstaber and Rees have recently extended this to all symmetric powers
\Sym^n(X) using their notion of the Frobenius -homomorphisms.
We give a simplification and a further extension of this theory, which is
based, rather unexpectedly, on results from super linear lgebra.Comment: LaTeX, 7 pages. Based on a talk at the Bialowieza meeting, July 200
C*-algebras associated with Hilbert C*-quad modules of finite type
A Hilbert -quad module of finite type has a multi structure of Hilbert
-bimodules with two finite bases. We will construct a -algebra from a
Hilbert -quad module of finite type and prove its universality subject to
certain relations among generators. Some examples of the -algebras from
Hilbert -quad modules of finite type will be presented.Comment: 35 page
A short proof of the Buchstaber-Rees theorem
We give a short proof of the Buchstaber-Rees theorem concerning symmetric
powers. The proof is based on the notion of a formal characteristic function of
a linear map of algebras.Comment: 11 pages. LaTeX2
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