Von Neumann modules have been \invented" in 2000 (preprint 1997). Every (pre-)Hilbert Hilbert module over a concrete (pre-)C-algebra B B(G) embeds in an essentially unique way into B(G;H) B(G H). There are many ways to make sure that a subspace E of B(G;H) is a concrete Hilbert module over a -subalgebra of B(G). No matter how this is attained, E is a von Neumann module if it is strongly closed in B(G;H). This is opposed with the denition of W-modules as self-dual Hilbert modules over a W-algebra|and, in fact, equivalent for every way we turn the W-algebra into a von Neumann algebra by choosing a faithful normal (nondegenerate) representation. We give an account what happened to and with von Neumann modules.
Von Neumann modules - and related topics
SKEIDE, Michael
2012-01-01
Abstract
Von Neumann modules have been \invented" in 2000 (preprint 1997). Every (pre-)Hilbert Hilbert module over a concrete (pre-)C-algebra B B(G) embeds in an essentially unique way into B(G;H) B(G H). There are many ways to make sure that a subspace E of B(G;H) is a concrete Hilbert module over a -subalgebra of B(G). No matter how this is attained, E is a von Neumann module if it is strongly closed in B(G;H). This is opposed with the denition of W-modules as self-dual Hilbert modules over a W-algebra|and, in fact, equivalent for every way we turn the W-algebra into a von Neumann algebra by choosing a faithful normal (nondegenerate) representation. We give an account what happened to and with von Neumann modules.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
