On operators factorizable through space
On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets
The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian...
An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and
Some combinatorial and probabilistic inequalities and their application to Banach space theory
Some combinatorial and probabilistic inequalities and their application to Banach space theory II
On the Kaczmarz algorithm of approximation in infinite-dimensional spaces
The Kaczmarz algorithm of successive projections suggests the following concept. A sequence of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and , where . We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.
Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)
Two results on continuity and boundedness of stochastic convolutions
Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.
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