Let $G$ be a locally compact group and let $1\le p<\infty .$ Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space $L^p\left(G\right)$ in terms of the weights. Sufficient and...

It is studied when inclusions between rearrangement invariant function spaces on the interval [0,∞) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions $L¹\cap L^{\infty }\hookrightarrow E$ and $E\hookrightarrow L¹+L^{\infty }$ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.

Disjointification inequalities are proven for arbitrary martingale difference sequences and conditionally independent random variables of the form ${f_k\left(s\right)x_k\left(t\right)}_{k=1}ⁿ$, where $f_k$’s are independent and xk’s are arbitrary random variables from a symmetric space X on [0,1]. The main results show that the form of these inequalities depends on which side of L₂ the space X lies on. The disjointification inequalities obtained allow us to compare norms of sums of martingale differences and non-negative random variables with...

Fissato lo spazio di Sobolev $H^{1,2}$ come ambiente del problema dinamico per un corpo viscoelastico unidimensionale si dimostra un teorema di unicità per la classe delle funzioni di rilassamento convesse. Si fa inoltre vedere come tale unicità sia strettamente legata allo spazio ambiente considerato.

In questa nota si completa la studio (iniziato in [1]) della caratterizzazione delle funzioni di rilassamento per le quali il problema dinamico della viscoelasticità lineare, con condizioni di spostamento nullo agli estremi, risulta ben posto nello spazio di Sobolev $H^{1,2}$. Precisamente, per un'opportuna classe di sollecitazioni esterne, si dimostra l'esistenza della soluzione, se le funzioni di rilassamento sono positive, convesse ed hanno il modulo di elasticità all'equilibrio strettamente maggiore...

It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann $\zeta$-function.

We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.

If X is a Banach space and C a convex subset of X*, we investigate whether the distance $d̂({\overline{co}}^{w*}\left(K\right),C):=supinf\left|\right|k-c\left|\right|:c\in C:k\in {\overline{co}}^{w*}\left(K\right)$ from ${\overline{co}}^{w*}\left(K\right)$ to C is M-controlled by the distance d̂(K,C) (that is, if $d̂({\overline{co}}^{w*}\left(K\right),C)\le Md̂(K,C)$ for some 1 ≤ M < ∞), when K is any weak*-compact subset of X*. We prove, for example, that: (i) C has 3-control if C contains no copy of the basis of ℓ₁(c); (ii) C has 1-control when C ⊂ Y ⊂ X* and Y is a subspace with weak*-angelic closed dual unit ball B(Y*); (iii) if C is a convex subset of X and X is considered canonically embedded into...

Let E be a Banach space and let $ℬ₁\left(B_{E*}\right)$ and $₁\left(B_{E*}\right)$ denote the space of all Baire-one and affine Baire-one functions on the dual unit ball $B_{E*}$, respectively. We show that there exists a separable L₁-predual E such that there is no quantitative relation between $dist(f,ℬ₁\left(B_{E*}\right))$ and $dist(f,₁\left(B_{E*}\right))$, where f is an affine function on $B_{E*}$. If the Banach space E satisfies some additional assumption, we prove the existence of some such dependence.