Latent Complete-Lattice Structure of Hilbert-Space Projectors
作者: Fedor Herbut
作者单位: 1Serbian Academy of Sciences and Arts
刊名: Quanta, 2019, Vol.8 (1), pp.1-10
来源数据库: Quanta
DOI: 10.12743/quanta.v8i1.85
原始语种摘要: To uncover the hidden complete-lattice structure of Hilbert-space projectors, which is not seen by the operator operations and relations (algebraically), resort is taken to the ranges of projectors (to subspaces—to geometry). Taking the range of a projector is completed into a bijection of all projectors onto all subspaces of any finite or countably infinite dimensional Hilbert space. As a second step, this basic bijection is upgraded into an isomorphism of partially ordered sets utilizing the sub-projector relation on the one hand, and the subspace relation on the other. As a third and final step, the basic bijection is further upgraded to isomorphism of complete lattices. The complete-lattice structure is derived for subspaces, then, using the basic bijection, it is transferred to the...
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  • bijection 双射
  • complete 实行
  • infinite 无穷的
  • algebraically 在代数学上
  • operator 话务员
  • isomorphism 同晶型
  • adjoint 伴随的
  • projector 投影式对准曝光装置
  • relation 关系
  • discrete 离散的