On the Strong McShane Integral of Functions with Values in a Banach Space

The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions.     

复平面上解析Banach空间的拟不变子空间

讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用,证明了Fock型空间F~p(C)={f∈Hol(C):1/π∫_C|f(z)|~pe~(-|z|~2)dA(z)+∞,1≤p+∞}与Hilbert空间H={f∈Hol(C):1/π∫_C|f(z)|~2e~(-|z|)dA(z)+∞}具有任意指标的拟不变子空间.     

On Weak Convergence of Probability Measures in a Banach Space

Necessary and sufficient conditions are obtained for weak convergence of Borel probability distributions in a separable strictly normed Banach space with a continuous modulus of convexity. These conditions are given in terms of simultaneous convergence of the distribution functions of the norm and of all linear continuous functionals with respect to the sequence of distributions under consideration. Bibliography: 9 titles.     

拟桶式空间的强对偶空间值的向量测度

证明了在某种紧性条件下拟桶式空间的强对偶空间值的向量测度的唯一存在性。     

On a Non-Periodic Modified Euler Equation: Well-Posedness and Quasi-Invariant Measures

Potential Analysis - We consider a modified Euler equation on $mathbb {R}^{2}$ . We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and...     

具拟不变测度群胚流上的交叉积

设G为第二可数局部紧有Haar系{λu}的群胚,A为G上左不变作用的交换群,则我们有C-动力系统（C（G）,A,β）．本文我们研究具有一定性质的拟不变测度,用此测度,得到了一些有关群胚C-代数及交叉积的重要结果,     

无RNP Banach空间中集值测度的Radon-Nikodym定理

自七十年代初以来关于集值测度的Radon-Nikodym导数取得了不少成果,所有这些成果中均要求所考虑的Banach空间具有RNP,本文在无RNP的Banach空间中建立了集值测度的Radon-Nikodym定理.     

THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a~2 in the case of n > 2.     

Directed Partial Orders on Complex Numbers and Quaternions over Non-Archimedean Linearly Ordered Fields

Let F be a non-archimedean linearly ordered field, and C and H be the field of complex numbers and the division algebra of quaternions over F, respectively. In this paper, a class of directed partial orders on C are constructed directly and concretely using additive subgroup of F ⁺. This class of directed partial orders includes those given in Rump and Wang (J. Algebra 400, 1–7, 2014), and Yang (J. Algebra 295(2), 452–457, 2006) as special cases and we conjecture that it covers all directed partial orders on C such that 1 > 0. It turns out that this construction also works very well on H. We note that none of these directed partial orders is a lattice order on C or H.     

Banach空间的p— Asplund 伴随空间

我们称一个定义在Banach空间E上的连续凸函数f具有Frechet可微性质（FDP）,如果E上的每个实值凸函数g≤f均在E一个稠密的Gδ－子集上Frechet可微。本文主要证明了：对任何Banach空间E,均存在一个局部凸相容拓扑p使得1）（E,p)是Hausdorff局部凸空间;2） E上的每个范数连续具有FDP的凸函数均是p－连续的;3）每个p-连续的凸函数均具有FDP ;4）p等价某个范数拓扑当且仅不E是Asplund空间。     

Non-Archimedean White Noise,Pseudodifferential Stochastic Equations,and Massive Euclidean Fields

We construct p-adic Euclidean random fields \(\varvec{\Phi }\) over \(\mathbb {Q}_{p}^{N}\), for arbitrary N, these fields are solutions of p-adic stochastic pseudodifferential equations. From a mathematical perspective, the Euclidean fields are generalized stochastic processes parametrized by functions belonging to a nuclear countably Hilbert space, these spaces are introduced in this article, in addition, the Euclidean fields are invariant under the action of certain group of transformations. We also study the Schwinger functions of \(\varvec{\Phi }\).     

Invertibility of Operator Matrices on a Banach Space

Let $\mathcal X $ and $\mathcal Y $ be Banach spaces, and let $A\in \mathcal B (\mathcal X )$ and $C\in \mathcal B (\mathcal Y , \mathcal X )$ be given operators. A necessary and sufficient condition is given for $\left[ \begin{array}{cc} A&C \\ X&Y \\ \end{array} \right]$ to be invertible (respectively, left invertible) for some $X\in \mathcal B (\mathcal X , \mathcal Y )$ and $Y\in \mathcal B (\mathcal Y )$ . Furthermore, some related results are obtained.     

Hilbert投影距离与Banach空间的范数

In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.     

Study of Frozen-Type Newton-Like Method in a Banach Space with Dynamics

Ukrainian Mathematical Journal - We perform the investigation of positives and negatives of the three-step iterative frozen-type Newton-like method for solving nonlinear equations in a Banach...