Let R be a prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R. An additive map D: R → R is called an α-derivation (or a skew derivation) on R if D(xy) = D(x)y + α(x)D(y) for all x, y \in R. An additive mapping F: R → R is called a generalized α-derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F(xy) = F(x)y + α(x)D(y) for all x, y \in R. We prove that, if F is a nonzero generalized skew derivation of R such that F(x)×[F(x), x]n = 0 for any x \in L, then either there exists λ \in C such that F(x) = λx for all x \in R, or R\subset M_{2}\left ( C \right ) and there exist a \in Qr and λ \in C such that F(x) = ax + xa + λx for any x \in R., Vincenzo De Filippis., and Obsahuje seznam literatury
This paper is mainly devoted to establishing an atomic decomposition of a predictable martingale Hardy space with variable exponents defined on probability spaces. More precisely, let (Ω,F, ℙ) be a probability space and p(·): Ω →(0,∞) be a F-measurable function such that 0 < {\inf _{x \in \Omega }}p(x) \leqslant {\sup _{x \in \Omega }}p(x) < \infty . It is proved that a predictable martingale Hardy space Pp(·) has an atomic decomposition by some key observations and new techniques. As an application, we obtain the boundedness of fractional integrals on the predictable martingale Hardy space with variable exponents when the stochastic basis is regular., Zhiwei Hao., and Obsahuje seznam literatury
Let H be a finite abelian group of odd order, D be its generalized dihedral group, i.e., the semidirect product of C2 acting on H by inverting elements, where C2 is the cyclic group of order two. Let Ω (D) be the Burnside ring of D, Δ(D) be the augmentation ideal of Ω (D). Denote by Δn(D) and Qn(D) the nth power of Δ(D) and the nth consecutive quotient group Δn(D)/Δn+1(D), respectively. This paper provides an explicit Z-basis for Δn(D) and determines the isomorphism class of Qn(D) for each positive integer n., Shan Chang., and Obsahuje seznam literatury
Let R be a prime ring of characteristic different from 2, Qr its right Martindale quotient ring and C its extended centroid. Suppose that F, G are generalized skew derivations of R with the same associated automorphism α, and p(x1, ..., xn) is a non-central polynomial over C such that \left[ {F(x),\alpha (y)} \right] = G(\left[ {x,y} \right]). for all x,y\in \left \{ p\left ( r_{1},...,r_{n} \right ):r_{1},...,r_{n}\in R\right \}. The there exist \lambda \in C such that F(x) = G(x) = λα(x) for all X\in R., Vincenzo De Filippis., and Obsahuje seznam literatury
Let X be a complex L1-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-α functions on the set ext B_{X*} of the extreme points of the dual unit ball B_{X*} to the whole unit ball B_{X*}. As a corollary we show that, given α \in [1, ω1), the intrinsic α-th Baire class of X can be identified with the space of bounded homogeneous Baire-α functions on the set ext B_{X*} when ext B_{X*} satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable L1-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015)., Pavel Ludvík, Jiří Spurný., and Obsahuje seznam literatury
We present simple proofs that spaces of homogeneous polynomials on Lp[0, 1] and ℓp provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976)., Seán Dineen, Jorge Mujica., and Obsahuje seznam literatury
We study G-almost geodesic mappings of the second type \mathop {{\pi _2}}\limits_\theta (e),\theta = 1,2 between non-symmetric affine connection spaces. These mappings are a generalization of the second type almost geodesic mappings defined by N. S. Sinyukov (1979). We investigate a special type of these mappings in this paper. We also consider e-structures that generate mappings of type \mathop {{\pi _2}}\limits_\theta (e),\theta = 1,2. For a mapping \mathop {{\pi _2}}\limits_\theta (e,F),\theta = 1,2 we determine the basic equations which generate them., Mića S. Stanković, Milan L. Zlatanović, Nenad O. Vesić., and Obsahuje seznam literatury