Costel Peligrad
Abstract
It is shown that every parareductive operator algebra $A \subset B(H)$ (as defined below) is a von Neumann algebra. For the proof of this result, some new properties of paraclosed operators are obtained. Finally, a sufficient condition that a reductive algebra be a von Neumann algebra is given.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
It is shown that every parareductive operator algebra $A \subset B(H)$ (as defined below) is a von Neumann algebra. For the proof of this result, some new properties of paraclosed operators are obtained. Finally, a sufficient condition that a reductive algebra be a von Neumann algebra is given.
Key concepts: Von Neumann algebra, Affiliated operator, Abelian von Neumann algebra, Mathematics, Jordan algebra, Von Neumann architecture, Linear subspace, Reflexive operator algebra