交换子空间格代数的自同构与插值性质

Automorphisms and Interpolation Properties of CSL Algebras

中文关键词:  交换子空间格  交换子空间格代数  自同构  插值

英文关键词:commutative subspace lattice  reflexive algebra  automorphism  interpolation.

中文摘要:

      本文第一部分用ＣＳＬ序区间投影集上的偏序给出ＣＳＬ代数自同构为拟空间实现的一个充分条件，作为推论，证明了代数自同构是拟空间实现的．第二部分，给出ＣＳＬ的序积与序和格代数的紧及有限插值性质，由此可得出一些非完全分配ＣＳＬ代数的插值性质。

英文摘要:

      In the first section, a sufficient condition under which every automorphism of a CSL algebra is quasi-spatial is given' As a corollary, it follows that every automorphism of a tree algebra defined in [6] is quasi-spatial. In the second section, we present the interpolation properties of compact and finite--rank operators in a CSL algebra corresponding to order product and order sum of CSL.