Interpolation of Operator Ideals with an Application to Eigenvalue Distribution Problems.
A Fredholm Determinant Theory for p-Summing Maps in Banach Spaces.
Diagonal and Convolution Operators as Elements of Operator Ideals.
On the Tensor Stability of s-Number Ideals.
Grenzordnungen von Operatorenidealen (II).
Grenzordnungen von Operatorenidealen (I).
On the eigenvalue spectrum of certain operator ideals
Isometric imbeddings of Euclidean spaces into finite dimensional -spaces
It is shown that imbeds isometrically into provided that n is a prime power plus one, in the complex case. This and similar imbeddings are constructed using elementary techniques from number theory, combinatorics and coding theory. The imbeddings are related to existence of certain cubature formulas in numerical analysis.
A formula for the eigenvalues of a compact operator
s-numbers, eigenvalues and the trace theorem in Banach spaces
Applications of spherical designs to Banach space theory
Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or -spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants...
Vorlesungen über numerisches Rechnen
Submultiplicative functions and operator inequalities
Let T: C¹(ℝ) → C(ℝ) be an operator satisfying the “chain rule inequality” T(f∘g) ≤ (Tf)∘g⋅Tg, f,g ∈ C¹(ℝ). Imposing a weak continuity and a non-degeneracy condition on T, we determine the form of all maps T satisfying this inequality together with T(-Id)(0) < 0. They have the form Tf = ⎧ , f’ ≥ 0, ⎨ ⎩ , f’ < 0, with p > 0, H ∈ C(ℝ), A ≥ 1. For A = 1, these are just the solutions of the chain rule operator equation. To prove this, we characterize the submultiplicative, measurable functions...
Vector-valued Lp-convergence of orthogonal series and Lagrange interpolation.
Spaces with maximal projection constants
We show that n-dimensional spaces with maximal projection constants exist not only as subspaces of but also as subspaces of l₁. They are characterized by a rigid set of vector conditions. Nevertheless, we show that, in general, there are many non-isometric spaces with maximal projection constants. Several examples are discussed in detail.
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