• Corpus ID: 20076423

Dependence of Kolmogorov widths on the ambient space

@article{Oikhberg2012DependenceOK,
  title={Dependence of Kolmogorov widths on the ambient space},
  author={Timur Oikhberg and M. N. Ostrovskiĭ},
  journal={arXiv: Functional Analysis},
  year={2012}
}
We study the dependence of the Kolmogorov widths of a compact set on the ambient Banach space. 

References

SHOWING 1-10 OF 53 REFERENCES
On banach spaces whose duals areL1 spaces
A structure theorem for Banach spaces whose duals areL1 spaces, is proved.
ASYMPTOTIC PROPERTIES OF KOLMOGOROV WIDTHS
  • M. Ostrovskii
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2010
Abstract We consider two problems concerning Kolmogorov widths of compacts in Banach spaces. The first problem is devoted to relations between the asymptotic behavior of the sequence of n-widths of a
A characterization of P1 spaces
Abstract A Banach space X is P 1 if and only if the radius of each bounded set in X is half its diameter.
New classes of L[p]-spaces
Preliminaries.- Geometrical implications of certain finite dimensional structures.- New classes of .- A class of .- A class of .
Entropy, Compactness and the Approximation of Operators
1. Entropy quantities 2. Approximation quantities 3. Inequalities of Bernstein-Jackson type 3. Inequalities of Berstein-Jackson type 4. A refined Riesz theory 5. Operators with values in C(X) 6.
Metric Entropy of the Grassmann Manifold
The knowledge of the metric entropy of precompact subsets of operators on finite dimensional Euclidean space is important in particular in the probabilistic methods developped by E. D. Gluskin and S.
Factorization of Linear Operators and Geometry of Banach Spaces
Absolutely summing operators and basic applications Factorization through a Hilbert space Type and cotype. Kwapien's theorem The ""abstract"" version of Grothendieck's theorem Grothendieck's theorem
Absolute Widths of Some Embeddings
The absolute widths of the natural identity operator Inpq, mapping lnp to lnq, for 1 � q � p � ∞, are considered. The main result of this work is the following:THEOREM 1. If 1 � q � p � ∞, 0 � m �
The finite-dimensionalPλ spaces with small λ
It is proved that there is a positive function Φ(∈) defined for sufficiently small ∈>0 such that lim∈→0 Φ(∈)=0 and for every integerk and everyk-dimensionalP1+∈ spaceE, d(E, l∞k)<1+Φ(∈).
DIAMETERS OF SETS IN FUNCTION SPACES AND THE THEORY OF BEST APPROXIMATIONS
CONTENTSIntroduction § 1. Survey of results which relate to special classes of functions § 2. A theorem on the diameters of a sphere § 3. Estimates from below of the diameters of the classes , , , ,
...
1
2
3
4
5
...