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1
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Weak Distances between Random Subproportional Quotients of $ℓ₁^{m}$

100%
Mankiewicz P.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2012
|
tom 60
|
nr 3
285-294
EN
Lower estimates for weak distances between finite-dimensional Banach spaces of the same dimension are investigated. It is proved that the weak distance between a random pair of n-dimensional quotients of $ℓ₁^{n²}$ is greater than or equal to c√(n/log³n).
2
Content available remote

Volumetric invariants and operators on random families of Banach spaces

64%
Mankiewicz P., Tomczak-Jaegermann N.
Studia Mathematica
|
2003
|
tom 159
|
nr 2
315-335
EN
The geometry of random projections of centrally symmetric convex bodies in $ℝ^{N}$ is studied. It is shown that if for such a body K the Euclidean ball $B₂^{N}$ is the ellipsoid of minimal volume containing it and a random n-dimensional projection $B = P_{H}(K)$ is "far" from $P_{H}(B₂^{N})$ then the (random) body B is as "rigid" as its "distance" to $P_{H}(B₂^{N})$ permits. The result holds for the full range of dimensions 1 ≤ n ≤ λN, for arbitrary λ ∈ (0,1).
3
Content available remote

On the geometry of proportional quotients of $l₁^{m}$

64%
Mankiewicz P., Szarek S.
Studia Mathematica
|
2003
|
tom 155
|
nr 1
51-66
EN
We compare various constructions of random proportional quotients of $l₁^{m}$ (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural "geometric" models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.
4
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Factoring the identity operator on a subspace of $l^{∞}_{n}$

38%
Mankiewicz P.
Studia Mathematica
|
1989-1990
|
tom 95
|
nr 2
133-139
5
Content available remote

A remark on Edgar's extremal integral representation theorem

32%
Mankiewicz P.
Studia Mathematica
|
1978
|
tom 63
|
nr 3
259-265
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