Frechet Algebra Research Articles

The symbols of a Frechet algebra of pseudodifferential operators on a polycylinder

H. O. Cordes investigated a C*-algebra C of singular integral operators on a polycylinder Ω=ℝn×B and defined symbol homomorphisms\(\sigma :C \to C(\mathbb{M}),\gamma :C \to CB(\mathbb{E},C_x )\) where\(\mathbb{M}\) is a certain compact space,\(\mathbb{E} = \partial \mathbb{B}^n \times \mathbb{R}_n \) and Cx is the Laplace comparison algebra of the compact space B (cf. [2]). We give a characterization of the Frechet algebra C∞⊂C obtained as the closure of a certain algebra of ψ dos in the topology generated by all HS norms. We define Bρ:L(HS)→L(HS)(ρɛS) by analogy with [4, 7] and prove that Bρ maps C into C∞ continuously. As a corollary we get\(\sigma (C_\infty ) = C(\mathbb{M})\), generalizing surjectivity results from [4] and [7]. It seems that no characterization of γ(C∞) is known, but it is clear that\(\gamma (C_\infty ) \subset CB(\mathbb{E},\mathcal{P}_\infty )\) where\(\mathcal{P}_\infty \) is the Frechet algebra studied in [1] and [7].

Coincidence of the homological dimensions of the Frechet algebra of smooth functions on a manifold with the dimension of the manifold

Coincidence of the homological dimensions of the Frechet algebra of smooth functions on a manifold with the dimension of the manifold

On the symbol homomorphism of a certain Frechet algebra of singular integral operators

We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L2-Sobolev norms. The proof is based on an ℝn of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation ∂u/∂t=i|D|ηu, 0<η<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.

Spectre de [formula omitted] pour des domaines bornés faiblement pseudoconvexes réguliers

If Ω is a weakly pseudoconvex domain in a Stein manifold, then the spectrum of the Frechet Algebra A ∞( \\ ̄ gW) is isomorphic to \\ ̄ gW, A ∞( \\ ̄ gW) denotes the space of holomorphic functions smooth up to the boundary. The spectrum of the uniform algebra A( \\ ̄ gW) is also isomorphic to -Ω. As a corollary we prove an approximation theorem for plurisubharmonic functions in Ω continuous in -Ω.

Multiplicative Functionals on Frechet Algebras with Bases

Let A denote a complex (or real) Fréchet algebra (i.e. a complete metrizable locally m-convex algebra, see [2] or [3]). It is known [2] that the topology of such an algebra can be defined by an increasing sequence [qn] (i.e. qn(x) ≦ qn+i(x) for all x £ A and n ≧ 1) of submultiplicative (i.e. qn(xy) ≦ qn(x)qn(y) for all x, 3/ Ç ^4 and for each n ≧ I) seminorms.

Accessible Points in the Spectrum of a Frechet Algebra

Accessible Points in the Spectrum of a Frechet Algebra

A Fréchet algebra example

A construction is given of a Fréchet algebra whose spectrum fails to be a k-space.

Codimension of Some Subspaces in a Frechet Algebra

Codimension of Some Subspaces in a Frechet Algebra