8 papers · 1 filter
On linearisation and existence of preduals
Karsten Kruse
We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properti…
On linearisation, existence and uniqueness of preduals: The isometric case
Karsten Kruse
We study the problem of existence and uniqueness of isometric Banach preduals of a Banach space. We derive necessary and sufficient conditions for the existence of an isometric Ban…
On linearisation and uniqueness of preduals
Karsten Kruse
We study strong linearisations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearisations are special preduals. A locally c…
Vector-valued holomorphic functions in several variables
Karsten Kruse
In the present paper we give some explicit proofs for folklore theorems on holomorphic functions in several variables with values in a locally complete locally convex Hausdorff spa…
Parameter dependence of solutions of the Cauchy-Riemann equation on spaces of weighted smooth functions
Karsten Kruse
We study the inhomogeneous Cauchy-Riemann equation on spaces of weighted -smooth -valued functions on an open set $Ω\subset\mathbb{R}^{…
On the nuclearity of weighted spaces of smooth functions
Karsten Kruse
Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vect…