RECENTLY Gowers and Maurey constructed the first example of Banach space containing no unconditional basic sequence. We denote this space by X_G, in this note. Using the results in ref. [1], some further studies and r...
supported by the Resources;Environmental Bureau, Chinese Academy of Sciences.
In China,rare earth elements(REE)are widely utilized in agriculture.Many studieson REE toxicology,pharmacology and biochemistry have been made both at home andabroad.However,REE damage to the functions of human memory...
In functional analysis, the following problem is fundamental: does every infinite-dimensional Banach space have an infinite-dimensional quotient space? It has remainedunsolved for a long time.
In [1], by using the classification theorem of finite simple groups, Xiao generalized a Zassenhaus’conjecture, and proved the following theorem. Theorem. Let G be a finite group. Then G is nilpotent if and only if (...
It is well known that a Grothendieck category having an Artinian generator is equivalent to Mod-A, where A is a suitable right Artinian ring. As an open problem, Albu and N(?)st(?)sescu asked in [1]: If is a Grothendi...
Project supported by the Science Fund of Academia Sinica
Let X be a finite set. A free monoid generated by X is denoted by X~*. Every element of X~* is called a word over X and every subset of X~* is called a language over X. The identity of X~*, so called empty word, is de...
For a right Noetherian ring R with 1, G0(R) and G1(R) denote the Grothendieck group K0((?)R) and the Whitehead group K1((?)R) respectively, where (?)R is the Abelian category of the finitely generated ri...
It is well known that every closed orientable 3-dimensional manifold is a 3-fold branched covering space of S3, and the branch set in S3 is a knot. Generally, this is best possible. For example, S1×F?(F? is an orient...
Let ■1 and ■2 be Banach spaces, with the norms ||·||1 and ||·||2 respectively. L is an operator from ■1 into ■2, f∈■2, we consider the following operator