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Can I read Commutants of Reflexive Algebras and Classification of Completely Distributive Subspace Lattices on EtoBox?
Commutants of Reflexive Algebras and Classification of Completely Distributive Subspace Lattices by Pengtong Li; Shijie Lu; Jipu Ma is a Mathematics article available to read on EtoBox.
What is Commutants of Reflexive Algebras and Classification of Completely Distributive Subspace Lattices about?
Let L \mathcal {L} be a subspace lattice on a normed space X X containing a nontrivial comparable element. If T T commutes with all the operators in Alg L \mbox {Alg}\mathcal {L} , then there exists a scalar λ \lambda such that ( T − λ I ) 2 = 0 (T-\lambda I)^2=0 . Furthermore, we classify the class of completely distributive subspace lattices into subclasses called Type I ( n ) I^{(n)} , Type I I ( n ) II^{(n)} and Type I I I III , respectively. It is shown that nontrivial nests or, more generally, completely distributive subspace lattices with a comparable element are Type I ( 1 ) I^{(1)} , and that nontrivial atomic Boolean subspace lattices are Type I I ( 0 ) II^{(0)} .
Who reads Commutants of Reflexive Algebras and Classification of Completely Distributive Subspace Lattices?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Pengtong Li; Shijie Lu; Jipu Ma
- Publisher
- American Mathematical Society (AMS)
- Published
- 2003
- Language
- EN
- Field
- Mathematics (Physical Sciences)