论文标题
融合结构和Hausdorff Uo-Lebesgue拓扑在操作员的矢量晶格代数
Convergence structures and Hausdorff uo-Lebesgue topologies on vector lattice algebras of operators
论文作者
论文摘要
Dedekind完整矢量晶格上的订单有限运算符的向量可以通过订单收敛的收敛结构，强订单收敛，无限制的订单收敛，强大的订单收敛性，以及适用于Hausdorff Uo-Lebesgue拓扑和强大的融合时的融合时，并与此类fortigence相关。我们确定了这六个汇合对阶数有限运算符和正常形态的含义的一般有效性。此外，研究了有限的操作员，订单连续运算符和正常形态上的左右相对于这些收敛结构的连续性，以及它们的同时连续性。相对于这些收敛结构的阶数有限运算符和正常形态的矢量sublattices的依从性，包括许多结果。这些是任意Dedekind完整矢量晶格的矢量议法的更一般结果的后果。通过解释其与矢量晶格的表示理论的相关性来激发对正常形态的矢量旋转的特别关注。
A vector sublattice of the order bounded operators on a Dedekind complete vector lattice can be supplied with the convergence structures of order convergence, strong order convergence, unbounded order convergence, strong unbounded order convergence, and, when applicable, convergence with respect to a Hausdorff uo-Lebesgue topology and strong convergence with respect to such a topology. We determine the general validity of the implications between these six convergences on the order bounded operator and on the orthomorphisms. Furthermore, the continuity of left and right multiplications with respect to these convergence structures on the order bounded operators, on the order continuous operators, and on the orthomorphisms is investigated, as is their simultaneous continuity. A number of results are included on the equality of adherences of vector sublattices of the order bounded operators and of the orthomorphisms with respect to these convergence structures. These are consequences of more general results for vector sublattices of arbitrary Dedekind complete vector lattices. The special attention that is paid to vector sublattices of the orthomorphisms is motivated by explaining their relevance for representation theory on vector lattices.
