一类格同态算子的刻画

Matrix Characterization of Riesz Homomorphism on Classical Banach Lattices

对Rn到Rm上的格同态算子进行矩阵刻画:每行至多有一个元素不为零且不为零的元素为正,并将此结论推广到经典Banach格c0,lp(1≤p<∞)到l∞(c或c0)的格同态算子的情况,并讨论了具有Schauder基的阿基米德Banach格上的格同态算子的矩阵特征。对于Rn按字典顺序作成的非阿基米德空间的情形指出上述了刻画及相应的结果不成立。

In this paper the characterization of lattice homomorphism from Rn to Rm is presented by means of the matrix with the property that there is at most one nonzero element which is necessarily positive in every row. Then this conclusion is generalized to the characterizations of Riesz homomorphism from classical Banach lattice c0,lp(1≤p≤∞)到l∞(c或c0). And the matrix characterization of Riesz homomorphism on Archimedean Banach lattices with the Schauder basis is discussed. Finally, it points out that the characterization and the related results do not hold for the non-Archimedean Riesz space Rn in the lexicographical order.