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On highly nonintegrable functions and homogeneous polynomials

100%
EN
We construct a sequence of homogeneous polynomials on the unit ball $𝔹_d$ in $ℂ^d$ which are big at each point of the unit sphere 𝕊. As an application we construct a holomorphic function on $𝔹_d$ which is not integrable with any power on the intersection of $𝔹_d$ with any complex subspace.
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Non-similarity of Walsh and trigonometric systems

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EN
We show that in $L_p$ for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.
3
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Greediness of the Haar system in rearrangement invariant spaces

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Extension of smooth subspaces in Lindenstrauss spaces

64%
EN
It follows from our earlier results [Israel J. Math., to appear] that in the Gurariy space G every finite-dimensional smooth subspace is contained in a bigger smooth subspace. We show that this property does not characterise the Gurariy space among Lindenstrauss spaces and we provide various examples to show that C(K) spaces do not have this property.
6
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On projections and unconditional bases in direct sums of Banach spaces

51%
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The space of multipliers into $l_1$

38%
8
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On complemented subspaces and unconditional bases in $l_{p}+l_{q}$

38%
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On projections in spaces of bounded analytic functions with applications

38%
10
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On linear properties of separable conjugate spaces of C*-algebras

38%
11
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On values of homogeneous polynomials in discrete sets of points

38%
12
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Existence of some special bases in Banach spaces

32%
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$H_{p}$-spaces, p≤1, and spline systems

32%
14
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On weakly compact operators from some uniform algebras

26%
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Some remarks on the Gurarij space

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