反正切Finsler度量与Randers度量射影等价(英文)

本文研究了反正切Finsler度量F=α+εβ+βarctan(β/α)与Randers度量F=α+β射影等价,这里α和α表示流形上的两个黎曼度量,β和β表示流形上的两个非零的1-形式.利用射影等价具有相同的Douglas曲率的性质,获得了这两类度量射影等价的充要条件.     

一类射影平坦的Finsler度量

本文主要研究由两个Riemann度量和一个1-形式构成的Finsler度量.首先,本文给出这类度量局部射影平坦的等价条件;其次,给出这类度量局部射影平坦且具有常旗曲率的分类情形;最后,构造这类度量局部射影平坦且具有常旗曲率K=-1的例子.     

度量射影的连续选择

本文讨论了集值映射的弱连续选择并应用于度量射影．设Y是Banach空间X的子空间且Y是可分的,在相差一个第一纲集的情况下,于弱拓扑下,支撑于Y上的度量射影是下半连续的并有连续选择．     

射影Ricci平坦的Kropina度量

本文研究和刻画了射影Ricci平坦的Kropina度量.利用Kropina度量的S-曲率和Ricci曲率的公式,得到了Kropina度量的射影Ricci曲率公式.在此基础上得到了Kropina度量是射影Ricci平坦度量的充分必要条件.进一步,作为自然的应用,本文研究和刻画了由一个黎曼度量和一个具有常数长度的Killing 1-形式定义的射影Ricci平坦的Kropina度量,也刻画了具有迷向S-曲率的射影Ricci平坦的Kropina度量.在这种情形下,Kropina度量是Ricci平坦度量.     

一些球对称射影平坦的Finsler度量的构造

研究刻画球对称Finsler度量的射影平坦性质的偏微分方程,通过对射影平坦Finsler度量PDE的研究,构造了两类球对称射影平坦Finsler度量,得到了一些球对称的射影平坦Finsler度量,并进一步给出这些Finsler度量的射影因子和旗曲率.     

一类射影平坦的球对称的芬斯勒度量

本文研究了射影平坦芬斯勒度量的构造问题.通过分析射影平坦的球对称的芬斯勒度量的方程的解,构造了一类新的射影平坦的芬斯勒度量,并得到了射影平坦的球对称的芬斯勒度量的射影因子和旗曲率.     

一类射影平坦的多项式(α，β)度量

讨论了一类具有如下形式的Finsler度量F=α+εβ+kβ~2/α+k~2β~4/3α~3-k~3β~6/5α~5,其中α=(a_(ij)y~iy~j)~(1/2)是一个Riemann度量,β=b_iy~i是一个1-形式,ε和k≠0是常数,研究了这类度量的旗曲率性质,得到了F为局部射影平坦的充要条件.     

一些射影平坦Finsler度量的构造

通过研究刻画Finsler度量的射影平坦性质的偏微分方程组,得到了一些有用的解, 进一步证明了其中的一些度量还具有零旗曲率.     

芬斯勒射影几何中的Ricci曲率

本文研究了保持Ricci曲率不变的Finsler射影变换。给定一个紧致无边的n维可微流形M，证明了：对于一个从M上的Berwald度量到Riemann度量的C-射影变换，如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率，则该射影变换是平凡的。     

射影平坦Finsler度量的解析构造

利用Hamel关于射影平坦的基本方程,我们导出了Randers度量的λ形变保持射影平坦的充分条件.特别,对一类具有特殊旗曲率性质的Randers度量我们证明了这类度量一定存在保持射影平坦性的λ形变.     

Strongly continuous spectral families

Summary We define a strongly continuous family & of bounded projections E(t), t real, on a Banach space X and show that & generates a densely defined closed linear transformation in X given by . T(&) has a real spectrum without eigenvalues and its resolvent operator satisfies a first order growth (G_i). If T₀ is a given closed linear trasformation defined a dense subset of X which has a purely continuous real spectrum and a resolvent operator satisfying the first order growth condition (G_i) then T₀ has a ? resolution of the identity ? &₀ consisting of closed projections E(t) in X. We show that if &₀ is also strongly continuous then T₀=T (&₀). Dedicated to the sixtieth birthday of Professor Edgar. R. Lorch     

Projections onto the set of Hankel matrices

The paper is devoted to lower estimates of the norms of the projections onto the set of Hankel matrices of order n. Let B_n be the set of operators in ² such that t_jk =0 for k+j>N and let Hank_N be the subspace in B_N consisting of those operators T for which t_jk =c_j+k (the Hankel matrices). The numbers _N are defined as the infimum of the norms of the projections of B_N onto Hank_N. The fundamental result of the paper asserts that.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 109–116, 1983.The author is grateful to V. V. Peller for stimulating discussions.     

Eine Charakterisierung der Boole'schen Algebra zu einer co -direkten Zerlegung

In this paper nuclear Boolean Algebras of projections in a locally convex space are considered. This are Boolean Algebras with special continuity properties, which are shared, for instance, by each bounded Boolean Algebra of projections in an ?^∞-space and by the algebra of each equicontinuos spectral measure in a nuclear space. It will be shown that a ?-complete nuclear Boolean Algebra leads to a c_o-direct sum of locally convex spaces and all the projections of the algebra belong to the complete algebra of projections of this c_o-direct partition. On the other hand if in a given locally convex space E there exists a nuclear complete Boolean Algebra of projections which has multiplicity one then each equicontinuos Boolean Algebra of projections in E is nuclear.     

Representing Yosida-Hewitt decompositions for classical and non-commutative vector measures

Let m be a bounded, real valued measure on a field of sets. Then, by the Yosida-Hewitt theorem, m has a unique decomposition into the sum of a countably additive and a singular measure. We show here that, in contrast to the classical arguments, this decomposition can be achieved by constructing the countably additive component. From this we obtain a simple formula for the countably additive part of a (strongly bounded) vector measure. We develop these ideas further by considering a weakly compact operator T on a von Neumann algebra M. It turns out that T has a unique decomposition into T_N +T_S, where T_S is singular, T_N is completely additive on projections and, for each x in M, there exists an increasing sequence of projections (p_n)(n = 1,2…), such that

T_N(x)=limT(p_nxp_n).

When M has a faithful representation on a separable Hilbert space, then we can fix a sequence of projections (p_n)(n = 1,2…) such that the above equation holds for every choice of x in M. For general M, there exists an increasing net of projections < q_F > such that, for every y in M,

lim_FT_N(y)−T(q_Fyq_F)=0.

     

Linear selections for the metric projection

A characterization is given of those proximinal subspaces of a normed linear space whose (set-valued) metric projections admit linear selections. This characterization is applied in each of the classical Banach spaces C₀(T) and L_p (1 ? p ? ∞), resulting in an intrinsic characterization of those one-dimensional subspaces whose metric projections admit linear selections.     

Projections of convex bodies and the fourier transform

The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the Busemann-Petty problem, characterizations of intersection bodies, extremal sections ofl _p-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the results mentioned above can be proved using similar methods. In particular, we present a Fourier analytic proof of the recent result of Barthe and Naor on extremal projections ofl _p-balls, and give a Fourier analytic solution to Shephard’s problem, originally solved by Petty and Schneider and asking whether symmetric convex bodies with smaller hyperplane projections necessarily have smaller volume. The proofs are based on a formula expressing the volume of hyperplane projections in terms of the Fourier transform of the curvature function.     

Minimal Lp projections by Fourier, Taylor, and Laurent series

In appropriate function space settings, it is proved that the Fourier, Taylor, and Laurent series projections are minimal in all L_p norms (1 p ∞). This result unifies and extends known results for the Fourier, Taylor, and Laurent projections in L_∞ and for the Fourier projection in L₁. The proof is based on a generalisation of a kernel summation formula due to Berman.     

Minimal projections on hyperplanes in sequence spaces

Summary The projection constants of hyperplanes in the classical sequence spaces (c ₀ ) and (l ₁ ) are determined, together with the projections of minimum norm. Entrata in Redazione I'll dicembre 1972.     

The Birman-Schwinger principle on the essential spectrum

Let H₀ and H be self-adjoint operators in a Hilbert space. We consider the spectral projections of H₀ and H corresponding to a semi-infinite interval of the real line. We discuss the index of this pair of spectral projections and prove an identity which extends the Birman-Schwinger principle onto the essential spectrum. We also relate this index to the spectrum of the scattering matrix for the pair H₀, H.