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1
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Isometric imbeddings of Euclidean spaces into finite dimensional $l_p$-spaces

100%
König H.
Banach Center Publications
|
1995
|
tom 34
|
nr 1
79-87
EN
It is shown that $l^n_2$ imbeds isometrically into $l^{n^2+1}_4$ 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.
2
Content available remote

Applications of spherical designs to Banach space theory

100%
König H.
Banach Center Publications
|
2004
|
tom 64
|
nr 1
127-134
EN
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 $ℓ_p$-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 can be estimated quite precisely.
3
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Submultiplicative functions and operator inequalities

64%
König H., Milman V.
Studia Mathematica
|
2014
|
tom 223
|
nr 3
217-231
EN
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 = ⎧ $(H∘f/H)f'^{p}$, f' ≥ 0, ⎨ ⎩ $-A(H∘f/H)|f'|^{p}$, 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 K on ℝ which are continuous at 0 and 1 and satisfy K(-1) < 0 < K(1). Any such map K has the form K(α) = ⎧ $α^{p}$, α ≥ 0, ⎨ ⎩ $-A|α|^{p}$, α < 0, with A ≥ 1 and p > 0. Corresponding statements hold in the supermultiplicative case with 0 < A ≤ 1.
4
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Spaces with maximal projection constants

64%
König H., Tomczak-Jaegermann N.
Studia Mathematica
|
2003
|
tom 159
|
nr 3
357-372
EN
We show that n-dimensional spaces with maximal projection constants exist not only as subspaces of $l_{∞}$ 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.
5
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On the eigenvalue spectrum of certain operator ideals

38%
König H.
Colloquium Mathematicum
|
1981
|
tom 44
|
nr 1
1-28
6
Content available remote

s-numbers, eigenvalues and the trace theorem in Banach spaces

32%
König H.
Studia Mathematica
|
1980
|
tom 67
|
nr 2
157-172
7
Content available remote

A formula for the eigenvalues of a compact operator

26%
König H.
Studia Mathematica
|
1979
|
tom 65
|
nr 2
141-146
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