(C)-半环范畴

建立了C—半环范畴的概念,讨论了C—半环范畴的一些基本性质,并且给出自由C—半环的一种构造方法,进而,给出了任意一族C—半环的积与上积的存在唯一性定理。     

The isometric extension problem between unit spheres of two separable Banach spaces

In this article, we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces. We obtain that under some condition the answer to this problem is affirmative.     

态射的广义Moore—Penrose逆

本文定义了态射的广义Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆，给出了它存在的一些充要条件，确定了它的一些表达式，推广了关于态射的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆的相应结果。     

The ε c -Product of a Schwartz b-Space by a Quotient Banach Space and Applications

We define the -product of a -space by a quotient Banach space. We give conditions under which this -product will be monic. Finally, we define the _c -product of a Schwartz b-space by a quotient Banach space and we give some examples of applications.     

Sets of uniqueness for spherically convergent multiple trigonometric series

A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.

     

On equivalence of derived categories

Let A be an Abelian category and B be a thick subcategory of A. Let D ^b(B) denote the derived category of cohomologically bounded chain complexes of objects in A and D _B ^b (A) denote the derived category of cohomologically bounded chain complexes of objects in A with cohomology in B. We give two if and only if conditions for equivalence of D(B) and D _B ^b (A), and we give an example where D ^b (B) and D _B ^b (A) are not equivalent.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.