COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

The authors prove that all n-th completely bounded cohomology groups of a nest algebra T(N) acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T(N)-bimodule containing the nest algebra. They also prove that Hcbn(A, M)(?)Hcbn(A, A) for all n≥1 and a CSL algebra A with an ultraweakly closed A-bimodule M containing A.     

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.     

Von Neumann代数中套子代数上的导子(Ⅱ)

本文主要研究因子ＶｏｎＮｅｕｍａｎｎ代数中套子代数上的导子。证明了由因子ＶｏｎＮｅｕｍａａｎ代数中套子代数到紧算子的任何导子都是内导子。     

Completely rank nonincreasing linear maps on nest algebras

In this paper, the completely rank nonincreasing bounded linear maps on nest algebras acting on separable Hilbert spaces are characterized, and an affirmative answer to a problem posed by Hadwin and Larson is given for the case of such nest algebras.

     

Additive Jordan derivations of reflexive algebras

Additive Jordan derivations of certain reflexive algebras are investigated. In particular, additive Jordan derivations of nest algebras on Banach spaces are shown to be additive derivations.     

套代数上的Jordan同构

本文主要研究了套代数上的Jordan同构.证明了套代数algβ和algγ之间的每一个Jordan同构　,要么是同构;要么是反同构.进而,存在可逆算子Y∈B（H）,使得对任意T∈algβ,要么　（T）=Y-1TY;要么　（T）=Y-1JT＊JY,这里J是一个共轭线性对合算子.     

Growth process and mechanism of a multi-walled carbon nanotube nest deposited on a silicon nanoporous pillar array

A large scale nest array of multi-walled carbon nanotubes (NACNTs) was grown on silicon nanoporous pillar array (Si-NPA) by thermal chemical vapor deposition. Through observing its macro/micromorphology and structure, ascertaining the catalyst component and its locations at different growth time by hiring field emission scanning electron microscopy, transmission electron microscopy (TEM), high-resolution TEM, and selected area electron diffraction, the growth process was deduced. Its thermal properties were also investigated by using a thermogravimetric analyzer. Our experiments demonstrated that the CNTs growth by means of root-growth mechanism at the initial growth stage, then a continuous growth process with its tip open is suggested, finally, a schematic growth model of NACNT/Si-NPA was presented.     

Commuting traces and commutativity preserving maps on triangular algebras

Let A be a triangular algebra. The problem of describing the form of a bilinear map satisfying B(x,x)x=xB(x,x) for all xA is considered. As an application, commutativity preserving maps and Lie isomorphisms of certain triangular algebras (e.g., upper triangular matrix algebras and nest algebras) are determined.     

Linear Maps Preserving the Closure of Numerical Range on Nest Algebras with Maximal Atomic Nest

Let be a maximal atomic nest on Hilbert space H and denote the associated nest algebra. We prove that a weakly continuous and surjective linear map preserves the closure of numerical range if and only if there exists a unitary operator such that for every or for every , where denotes the transpose of T relative to an arbitrary but fixed base of H. As applications, we get the characterizations of the numerical range or numerical radius preservers on . The surjective linear maps on the diagonal algebras of atomic nest algebras preserving the closure of numerical range or preserving the numerical range (radius) are also characterized. Submitted: January 3, 2001?Revised: December 2, 2001