实Banach代数的表示

本文研究了对任意厄米实Banach*-代数的表示理论进行系统研究. 利用对该类代数所定义的一般态空间展开讨论. 获得了该类代数上可表示泛函的一系列好的性质,进而给出了不可约表示的等价刻画.这些结果将Naimark、Gaur等人的工作进行了推广.     

BANACH ALGEBRAS WITH LARGE GROUPS OF UNITARY ELEMENTS

We study unitary Banach algebras, as defined by M. L. Hansenand R. V. Kadison in 1996, as well as some related conceptslike maximal or uniquely maximal Banach algebras. We show thata norm-unital Banach algebra is uniquely maximal if and onlyif it is unitary and has minimality of the equivalent norm.We prove that every unitary semisimple commutative complex Banachalgebra has a conjugate-linear involution mapping each unitaryelement to its inverse, and that, endowed with such an involution,becomes a hermitian *-algebra. The possibility of removing therequirement of commutativity in the above statement is alsoconsidered. The paper concludes by translating to real algebrassome results previously known in the complex case. In particular,we show that every maximal semisimple finite-dimensional realBanach algebra is isometrically isomorphic to a real C*-algebra.     

DEGENERATION OF SEMISIMPLE ALGEBRAS

Some observations and conjectures concerning finite dimensional associative commutative algebras that are degenerations of semisimple algebras.

“…on sait qu'on ne sait rien sur cette sorte d'algèbre.” André Weil     

Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

RESTRICTIONS OF LARGE IRREDUCIBLE REPRESENTATIONS OF THE CLASSICAL GROUPS TO NATURALLY EMBEDDED SMALL SUBGROUPS CANNOT BE SEMISIMPLE

It is proved that the restriction of a p-restricted representation of a classical algebraic group G of rank r in characteristic p > 0 to a naturally embedded semisimple subgroup cannot be completely reducible (semisimple) if the subgroup has a simple component of rank m small enough with respect to r and the highest weight is large enough with respect to p. It suffices to assume that r ≥ 2m and that the highest weight is equal to ∑ ^r _i=1 a_i ω _i with ∑ ^r _i=1 a_i ≥ 2p ? 1 if p ≠ 2 or G ≠ C_r (K) and ∑ ^r _i=1 a_i ≥ 4 for p = 2 and G = C_r (K).     

半单李代数的一个特征性质

本文给出了中心为零的带非退化对称不变双线性型的有限维李代数的若干性质,并由此给出了半单李代数的一个新刻划。     

CLASSIFICATION OF FINITE GROUPS GENERATED BY REFLECTIONS AND ROTATIONS

We classify finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two. These groups naturally arise in the study of the quotient of a Euclidean space by a finite orthogonal group and hence in the theory of orbifolds.     

FINITE DIMENSIONAL REPRESENTATIONS OF u-HOPF ALGEBRAS

Splitting trace modules of u-Hopf algebras are characterized. As an example, all finite dimensional splitting trace modules of the restricted form U_t (sl ₂) are classified. The semisimplicity of a representation V from that of tensor product V ? M in _H M for u-Hopf algebra H is given.     

POINTED REPRESENTATIONS OFINFINITE DIMENSIONAL LIE ALGEBRAS

ＰＯＩＮＴＥＤＲＥＰＲＥＳＥＮＴＡＴＩＯＮＳＯＦＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＬＩＥＡＬＧＥＢＲＡＳ￥ＸＵＸＩＡＮＧＡｂｓｔｒａｃｔ：ＡｃｏｎｔｒａｖａｒｉｅｄｂｉｌｉｎｅａｒｐａｉｒｉｎｇＸｏｎｅｖｅｒｙＭ（ρ）×Ｍ（ρθ）ｉｓｄｅｔｅｒｍ...     

ISOMETRIC ISOMORPHISMS OF TRIANGULAR BANACH ALGEBRAS

§ 1　 IntroductionLet Aand Bbe Banach algebras.Let Mbe a Banach A,B-module with bounded1 .Thatis,‖AMB‖≤‖A‖‖M‖‖B‖ for each A∈A,B∈Band M∈M.ThenT=A M0 B=A M0 B :A∈ A,B∈ B,M∈ Mis a Banach algebra with the usual operations and the normA M0 B =‖ A‖ ‖ M‖ ‖ B‖ .We call such an algebra a triangular Banach algebra.In[1 ] ,the derivation of triangular Ba-nach algebras is studied and the firstcohomology groups ofsome special triangular Banachalgebras are explicitl…     

GROUPS OF AUTOMORPHISMS OF CHEVALLEY ALGEBRAS

In the paper we present an extension of Segal theorem on Lie algebra automorphisms of upper triangular nilpotent matrices to the whole class of nilpotent subalgebras generated by positive parts of indecomposable Chevalley algebras.     

APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

For a Banach algebra A,we denote by A* and A** the first and the second duals of A respectively.Let T be a mapping from A* to itself.In this article,we will investigate some stability results concernin...     

由具奇异系数的强椭圆微分算子生成的解析半群

本文提出了低阶项系数具一定奇异性的高阶强椭圆微分算子生成解析半群的条 件,其包含了低阶项系数属于Schecter位势类的情形.特别地,低阶项系数属于LP(Rn) 的情形也在其中.作为应用,得到低阶项系数属于LP(Rn)的强椭圆算子的相应半群生 成,且p还可取到一些临界值.     

REPRESENTATIONS OF SOLVABLE LIE GROUPS AND GEOMETRIC QUANTIZATION

1.IntroductionTheorbitmetheodpresentedbyKirillovandKostanthajsgreatlybeendevelopedrecentlytorealizerepresentationsofgroups(finiteandinfinite-dimensionalgroups).Italsohascloserelationshipswiththeclassificationofrepresentationsl'].Infact,thedeeporiginoftheorbitmetheodisgeometricquantization.Theproblemofgeometricquantizationis,startingfromthegeometryofasymplecticmanifold(M,w)whichgivesthemodelofaclassicalmechenicalsystem,toconstructaHilbertspaceHandasetofoperatorsonitwhichgivethequantumanalogue…     

自反Banach空间上算子代数的超自反性

本文引入自发Banach空间上算子代数A的超自反定义，讨论了A超自反的充要条件，超自反常数的估计以及超自反在代数同构下的不变性。