Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

自伴算子代数上的某些*-自同态的σ-弱混合性

设A是希尔伯特空间H上的自伴算子代数,α是A上的*-自同态.如果存在单位向量e∈H,使得对任意α∈A和单位向量h∈H,有lim_(n→∞)〈α~n(a)h,h〉=〈αe,e〉成立,那么称α是A上的σ-弱混合的*-自同态.本文研究了这一有趣性质,并得到了一个*-自同态是σ-弱混合的充分条件.     

等距算子的延拓、逼近及相关问题

本文介绍了等距算子从单位球面、从区域及从保距离1等条件下的各种等距廷拓问题；并介绍了(线性与非线性算子)等距算子的弱扰动、强扰动及渐近等距算子等问题．文中从历史到现状，概括了重要的研究结果，并指出了一些尚未解决的遗留问题．     

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.

     

赋β-范空间中单位球面间的等距算子的线性延拓

本文得到了等距映射的线性延拓的一般结果:设E,F是赋范(或β-严格凸赋β-范)线性空间,若V_0:S_1(E)→S_1(F)是等距,且对任意的x,y∈S_1(E),有‖V_0x-|(?)|V_0y‖≤‖x-|(?)|y‖,(?)∈R,则V_0必可延拓到全空间上等距算子(或线性等距算子)。特别,当E,F是赋范线性空间,V_0是满射或F为严格凸空间时,则V_0必可延拓为全空间的线性等距算子,从而推广了文[3～5]中的相应结果。     

Mappings on Spaces of Continuous Functions

Let X and Y be locally compact Hausdorff spaces and T : C₀(X) C₀(Y) a ring homomorphism. We completely characterize such homomorphisms and show that if T is R-linear, then T is either C-linear or C-antilinear. In any case T is continuous and there is a continuous map : Y X such that Tf = f o , f C₀(X) (if T is C-linear) or (if T is C-antilinear). Thus, extending a result of Mólnar, we also derive the general form of an isometry T.AMS Subject Classification (2000): primary 46J05, 46E25(deceased) Passed away on 24 May 1999.     

Isometries of Quaternionic Lie Groups

We study connected Lie groups whose Lie algebra is obtained as the tensor product of a real associative algebra and the algebra of quaternions. It is proved that they carry a natural integrable -structure. We endow such quaternionic Lie groups with a left-invariant Hermitian metric and study the identity connected component of their isometry groups. The determination of such identity connected component is illustrated with a family of examples.     

Similarity to an isometry of a composition operator

We study the composition operators which are similar to an isometry on the classical Hardy space .

     

On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.