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

100%

Mankiewicz P.

tom 60

nr 3

285-294

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).

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

63%

Mankiewicz P. , Szarek S.

tom 155

nr 1

51-66

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.

Volumetric invariants and operators on random families of Banach spaces

63%

Mankiewicz P. , Tomczak-Jaegermann N.

tom 159

nr 2

315-335

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).

Factoring the identity operator on a subspace of $l^{∞}_{n}$

38%

Mankiewicz P.

Studia Mathematica

1989-1990

tom 95

nr 2

133-139

A remark on Edgar's extremal integral representation theorem

32%

Mankiewicz P.

Studia Mathematica

1978

tom 63

nr 3

259-265