A Fréchet space with a sequence ${{\left|\right|·\left|\right|}_k}_{k=1}^{\infty }$ of generating seminorms is called tame if there exists an increasing function σ: ℕ → ℕ such that for every continuous linear operator T from into itself, there exist N₀ and C > 0 such that ${\left|\right|T\left(x\right)\left|\right|ₙ\le C\left|\right|x\left|\right|}_{\sigma \left(n\right)}$ ∀x ∈ , n ≥ N₀. This property does not depend upon the choice of the fundamental system of seminorms for and is a property of the Fréchet space . In this paper we investigate tameness in the Fréchet spaces (M) of analytic functions on Stein manifolds M equipped with the compact-open...

We discuss recent developments in the study of the homotopy classes for the Sobolev spaces $W^{1,p}\left(M;N\right)$. In particular, we report on the work of H. Brezis - Y. Li [5] and F.B. Hang - F.H. Lin [9].

The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property $\left(L{B}^{\infty }\right)$ for the dual space of the space of germs of holomorphic functions on that compact set.

The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra $s_{•}$. This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras...