68,579 research outputs found

### Uncountable sets of unit vectors that are separated by more than 1

Let $X$ be a Banach space. We study the circumstances under which there
exists an uncountable set $\mathcal A\subset X$ of unit vectors such that
$\|x-y\|>1$ for distinct $x,y\in \mathcal A$. We prove that such a set exists
if $X$ is quasi-reflexive and non-separable; if $X$ is additionally
super-reflexive then one can have $\|x-y\|\geqslant 1+\varepsilon$ for some
$\varepsilon>0$ that depends only on $X$. If $K$ is a non-metrisable compact,
Hausdorff space, then the unit sphere of $X=C(K)$ also contains such a subset;
if moreover $K$ is perfectly normal, then one can find such a set with
cardinality equal to the density of $X$; this solves a problem left open by S.
K. Mercourakis and G. Vassiliadis.Comment: to appear in Studia Mat

### Untapped Instrument. Sovereign Wealth Funds and Chinese policy toward the Central and Eastern European countries

Although there has been vivid academic debate as to what extent Sovereign Wealth Funds (SWFs) are motivated by political reasons, it is rather clear that countries can use state-owned investment funds as a tool of their foreign policy. Even Barack Obama, during his initial presidential campaign in 2008 commented: “I am obviously concerned if these… sovereign wealth funds are motivated by more than just market consideration and that’s obviously a possibility”.
This book looks at SWF activities in Central and Eastern Europe (CEE) to determine the main motives for SWF presence in CEE. Are the potential financial gains the only reason behind their investments? Are SWF activities in the region dangerous for the stability and security of the CEE countries?
The book is pioneering analyses of SWFs behaviour in the region, based on empirical data collected from the Sovereign Wealth Fund Institute Transaction Database, arguably the most comprehensive and authoritative resource tracking SWF investment behaviour globally.Rozdział pochodzi z książki: Political Players? Sovereign Wealth Funds’ Investments in Central and Eastern Europe, T. Kamiński (ed.), Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2017.This chapter aims at looking at the role of Sovereign wealth funds (SWFs)
in China’s policy toward Central and Eastern European (CEE) countries
in the 21st century, especially since the enlargement of the European Union
(EU) in 2004. During this time, we could observe an increase of Chinese
interest in the region resulting in growing trade, investments and number
of contacts on all levels. China has used a wide array of different instruments
to achieve its goals in the region: from a big political project such as the “16+1
format” to an unprecedented frequency of contacts between Chinese
provinces and their European counterparts (Kaczmarski, Jakóbowski
2015). Despite a visible growth of economic ties, Beijing presented a very
limited will to use investments as a political instrument. Even if Chinese
investments in CEE are booming, they are possibly less politically biased
and more market-driven than those in other developing countries, like
African ones.This book was published in frames of project “Political significance of the Sovereign Wealth
Funds’ investments in the Central and Eastern Europe”. The project was financed by the Polish
National Science Centre (Decision no. DEC-2012/07/B/HS5/03797)

### The ideal of weakly compactly generated operators acting on a Banach space

We call a bounded linear operator acting between Banach spaces weakly
compactly generated ($\mathsf{WCG}$ for short) if its range is contained in a
weakly compactly generated subspace of its codomain. This notion simultaneously
generalises being weakly compact and having separable range. In a comprehensive
study of the class of $\mathsf{WCG}$ operators, we prove that it forms a closed
surjective operator ideal and investigate its relations to other classical
operator ideals. By considering the $p$th long James space
$\mathcal{J}_p(\omega_1)$, we show how properties of the ideal of
$\mathsf{WCG}$ operators (such as being the unique maximal ideal) may be used
to derive results outside ideal theory. For instance, we identify the
$K_0$-group of $\mathscr{B}(\mathcal{J}_p(\omega_1))$ as the additive group of
integers

### On ergodicity of some Markov processes

We formulate a criterion for the existence and uniqueness of an invariant
measure for a Markov process taking values in a Polish phase space. In
addition, weak-$^*$ ergodicity, that is, the weak convergence of the ergodic
averages of the laws of the process starting from any initial distribution, is
established. The principal assumptions are the existence of a lower bound for
the ergodic averages of the transition probability function and its local
uniform continuity. The latter is called the e-property. The general result is
applied to solutions of some stochastic evolution equations in Hilbert spaces.
As an example, we consider an evolution equation whose solution describes the
Lagrangian observations of the velocity field in the passive tracer model. The
weak-$^*$ mean ergodicity of the corresponding invariant measure is used to
derive the law of large numbers for the trajectory of a tracer.Comment: Published in at http://dx.doi.org/10.1214/09-AOP513 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org

### Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Let $L=\Delta^{\alpha/2}+ b\cdot\nabla$ with $\alpha\in(1,2)$. We prove the
Martin representation and the Relative Fatou Theorem for non-negative singular
$L$-harmonic functions on ${\mathcal C}^{1,1}$ bounded open sets.Comment: 28 pages, editorial change

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