During the last years the dynamics of linear operators on infinite dimensional spaces has been extensively studied, see the survey articles [3], [6], [7], [8], [9], [11]. Let us recall the notion of hypercyclicity. Let X be a separable Banach space and T : X → X be a bounded linear operator. The operator T is said to be hypercyclic provided there exists a vector x ∈ X such that its orbit under ...

Let G be a monoid that acts on topological space X by homeomorphisms such there is point x0∈X with GU=X for each neighbourhood U of x0. A subset said to G-bounded if x0 finite F A⊆FU. We prove metrizable and separable G-space X, the bounded subsets are completely determined any dense subspace. also obtain sufficient conditions locally G-bounded, which apply groups. Thereby, we extend some previ...

(A) We study in this paper topological properties of conjugacy classes in Polish groups. There are two questions which we are particularly interested in. First, does a Polish group G have a dense conjugacy class? This is equivalent (see, e.g., Kechris [95, 8.47]) to the following generic ergodicity property of G: Every conjugacy invariant subset A ⊆ G with the Baire property (e.g., a Borel set)...

A self-consistent mean-field theory for bosons for T > 0 is used to reconcile predictions of collapse with recent observations of Bose-Einstein condensation of Li. Eigenfunctions of a (non-separable) Hamiltonian that includes the anisotropic external trap field and atom-atom interactions are obtained by an iteration process. A sum over the Bose distribution, and the “alternating direction impli...

Recently, relaxed belief propagation and approximate message passing have been extended to apply to problems with general separable output channels rather than only to problems with additive Gaussian noise. We apply these to estimation of signals from quantized samples with minimum mean-squared error. This provides a remarkably effective estimation technique in three settings: an oversampled de...

The D-meson properties in dense nuclear matter are studied. The D-meson spectral density is obtained within the framework of a coupled-channel self-consistent calculation assuming, as bare meson-baryon interaction, a separable potential. The Λc(2593) resonance is generated dynamically in our coupled-channel model. The medium modifications of the D-meson properties due to Pauli blocking and the ...

In this paper we consider MIMO broadcast channels with separable variance profile modelling antenna correlation at both transmit and receive sides. For large number of antennas we derive the theoretical sum-rate capacity when the transmitter performs zero-forcing or regularized zero-forcing precoding. In particular, we apply the results to volumelimited devices where the correlation originates ...

For two not necessarily commutative topological groups G and T , let H(G, T ) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G, T ) is a k-space. As a consequence we obtain that if G1 is a dense subgroup of G then H(G1, T ) is homeomorphic to H(G,T ), and if G is separable h-complete, then the...

Abstract A topological space is iso-dense if it has a dense set of isolated points, and scattered each its non-empty subspaces an point. In $$\textbf{ZF}$$ ZF (i.e. Zermelo–Fraenkel theory without the Axiom Choice ( $$\textbf{AC}$$ AC )), basic properties spaces are investigated. new permutat...

It is shown that for every closed, convex and nowhere dense subset C of a superreflexive Banach space X there exists a Radon probability measure μ on X so that μ(C + x) = 0 for all x ∈ X. In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a clos...