An example on ordered Banach algebras

Let be a complex unital Banach algebra. We consider the Banach algebra ordered by the algebra cone , and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in .

     

Cn中单位球上$mu$-Bloch函数的等价刻画

设$\mu$是$[0,1)$上的正规函数, 给出了${\bf C}^{\it n}$中单位球$B$上$\mu$-Bloch空间$\beta_{\mu}$中函数的几种刻画. 证明了下列条件是等价的: (1) $f\in \beta_{\mu}$; \ (2) $f\in H(B)$且函数$\mu(|z|)(1-|z|^{2})^{\gamma-1}R^{\alpha,\gamma}f(z)$ 在$B$上有界; (3) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{1}-1}\frac{\partial^{M_{1}} f}{\partial z^{m}}(z)}$ 在$B$上有界, 其中$|m|=M_{1}$; (4) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{2}-1}R^{(M_{2})}f(z)}$ 在$B$上有界.     

Weak amenability of triangular Banach algebras

Let and be unital Banach algebras, and let be a Banach -module. Then becomes a triangular Banach algebra when equipped with the Banach space norm . A Banach algebra is said to be -weakly amenable if all derivations from into its dual space are inner. In this paper we investigate Arens regularity and -weak amenability of a triangular Banach algebra in relation to that of the algebras , and their action on the module .

     

Tangentially positive isometric actions and conjugate points

Let be a complete Riemannian manifold with no conjugate points and a principal -bundle, where is a Lie group acting by isometries and the smooth quotient with the Riemannian submersion metric.

We obtain a characterization of conjugate point-free quotients in terms of symplectic reduction and a canonical pseudo-Riemannian metric on the tangent bundle , from which we then derive necessary conditions, involving and , for the quotient metric to be conjugate point-free, particularly for a reducible Riemannian manifold.

Let , with the Lie Algebra of , be the moment map of the tangential -action on and let be the canonical pseudo-Riemannian metric on defined by the symplectic form and the map , . First we prove a theorem, stating that if is not positive definite on the action vector fields for the tangential action along then acquires conjugate points. (We proved the converse result in 2005.) Then, we characterize self-parallel vector fields on in terms of the positivity of the -length of their tangential lifts along certain canonical subsets of . We use this to derive some necessary conditions, on and , for actions to be tangentially positive on relevant subsets of , which we then apply to isometric actions on complete conjugate point-free reducible Riemannian manifolds when one of the irreducible factors satisfies certain curvature conditions.

     

区组长为奇素数的自反MD设计 (英)

本文利用差方法对自反MD设计SCMD$(4mp, p,1)$的存在性给出了构造性证明, 这里$p$为奇素数, $m$为正整数.     

Geometry of Banach spaces having shrinking approximations of the identity

Let and let be a compact set of scalars. We introduce property of Banach spaces by the requirement that whenever is a bounded net converging weak to in and . Using with 1$">, we characterize the existence of certain shrinking approximations of the identity (in particular, those related to -, -, and -ideals of compact or approximable operators). We also show that the existence of these approximations of the identity is separably determined.

     

Choquet representability of submodular functions

Mathematical Programming - Let $$\Omega $$ be an arbitrary set, equipped with an algebra $${\mathcal {A}}\subseteq 2^{\Omega }$$ and let $$f: B({\mathcal {A}}) \rightarrow {\mathbb {R}}$$ be a...     

A Note on Bifurcation for Harmonic Maps on Annular Domains

Mediterranean Journal of Mathematics - In this paper we consider harmonic maps u(r, θ) from an annular domain $${\Omega _{\rho} = B_{1}\backslash\bar{B}_{\rho}}$$ to S 2 with the boundary...     

Nullification and cellularization of classifying spaces of finite groups

In this note we discuss the effect of the -nullification and the -cellularization over classifying spaces of finite groups, and we relate them with the corresponding functors with respect to Moore spaces that have been intensively studied in the last years. We describe by means of a covering fibration, and we classify all finite groups for which is -cellular. We also carefully study the analogous functors in the category of groups, and their relationship with the fundamental groups of and

     

Weighted estimates of Calderon’s commutators on complex plane

Let V(z) be a complex-valued function on the complex plane ℂ satisfying the condition |V(z) − V(ζ)| ≤ w|z − ζ|, z, ζ ε ℂ; ω ≥ 0 be a Muckenhoupt A _p weight on ℂ; i.e., the inequality

The Ground State Solutions for Kirchhoff-Schr¨odinger Type Equations with Singular Exponential Nonlinearities in RN*

In this paper, the authors consider the following singular Kirchhoff-Schr¨odinger problem M Z RN |u|N + V (x)|u|N dx (N u + V (x)|u|N?2u) = f(x, u) |x|η in RN , (Pη) where 0 < η < N, M is a Kirchhoff-type function and V (x) is a continuous function with positive lower bound, f(x, t) has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates, they get the existence of ground state solution for (Pη). Moreover, they also get the same result without the A-R condition.     

A Trudinger–Moser inequality for a conical metric in the unit ball

Archiv der Mathematik - In this note, we prove a Trudinger–Moser inequality for a conical metric in the unit ball. Precisely, let $${\mathbb {B}}$$ be the unit ball in $${\mathbb {R}}^N$$...     

Über die Primteiler-Anzahl ω(n)

It is shown by analytical means that, if one assumes the Riemann hypothesis, the asymptotic formula $$\sum\limits_{n \leqslant x} {\omega (n) = x 1n1n } x + B - x\int_l^{x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } {\frac{{\{ t\} }}{{t^2 (1n x - 1n t)}}dt + O(x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon } )} $$ holds. This improves a result ofB. Saffari, who got a weaker error term by using the Dirichlet “hyperbola method”. The above formula, in turn, implies the Riemann hypothesis.     

Weak law of large numbers for iterates of random-valued functions

Aequationes mathematicae - Given a probability space $$ (\Omega , {\mathcal {A}}, P) $$ , a complete and separable metric space X with the $$ \sigma $$ -algebra $$ {\mathcal {B}} $$ of all its...     

自伴算子空间上保持Jordan积投影的线性映射

Let Bs(H) be the real linear space of all self-adjoint operators on a complex Hilbert space H with dim H ≥ 2.It is proved that a linear surjective map on Bs (H) preserves the nonzero projections of Jordan products of two operators if and only if there is a unitary or an anti-unitary operator U on H such that (X)=λU XU,X∈Bs(H) for some constant λ with λ∈{1,1}.     

A note on invertibility preservers on Banach algebras

Let be be semisimple Banach algebras and let be a unital bijective linear operator that preserves invertibility. If the socle of is an essential ideal of , then is a Jordan isomorphism.

     

多元线性模型中的有偏估计

刘金山在1999年给出了多元线性模型参数分量βi和参数矩阵B的有偏估计β1=(X'X)-1YCi,i=1,…,m和B=(β1,β2,…,βm)以及βi的性质.本文从另一角度得到了同样的估计,证明了刘金山文中所给的两个检验是UMP检验,估计βi是βi的线性可容许估计,证明了B不是B的可容许估计,由此给出了两种改进估计.     

An operator inequality related to Jensen's inequality

For bounded non-negative operators and , Furuta showed

We will extend this as follows: implies

where is a harmonic mean of and . The idea of the proof comes from Jensen's inequality for an operator convex function by Hansen-Pedersen.

     

由双边群相关Hopf模诱导的Morita等价

Let H be a Hopf π-coalgebra over a commutative ring k with bijective antipode S, and A and B right π-H-comodulelike algebras. We show that the pair of adjoint functors （F3 = A  Bop A□ HBop -,G3 = （-）coH） between the categories A□HBopM and AMπB-H is a pair of inverse equivalences, when A is a faithfully flat π-H-Galois extension. Furthermore, the categories Moritaπ-H（A,B） and Morita □π-H（AcoH,BcoH） are equivalent, if A and B are faithfully flat π-H-Galois extensions.