High Quality Content by WIKIPEDIA articles! The Schroder–Bernstein theorem, from set theory, has analogs in the context operator algebras. This article discusses such operator-algebraic results. Suppose M is a von Neumann algebra and E, F are projections in M. Let ~ denote the Murray-von Neumann equivalence relation on M. Define a partial order « on the family of projections by E « F if E ~ F' ? F. In other words, E « F if there exists a partial isometry U ? M such that U*U = E and UU* ? F. Suppose M is a von Neumann algebra and E, F are projections in M. Let ~ denote the Murray-von Neumann equivalence relation on M. Define a partial order « on the family of projections by E « F if E ~ F' ? F. In other words, E « F if there exists a partial isometry U ? M such that U*U = E and UU* ? F. For closed subspaces M and N where projections PM and PN, onto M and N respectively, are elements of M, M « N if PM « PN.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.