Operator Algebrae/Von Neumann algebrae

The operator algebra operator algebra Let be a Banach space over the field or . Consider the set of bounded and linear functions from to itself. This Operator topologies Topologies on a Banach space weak topology Let be a Banach space, and let be its dual space. The weak topology on is defined to be the initial topology with respect to the maps , where ranges over . properties of the weak topology Topologies exclusively for operator spaces bounded operators on a normed space form a Banach space under norm topology Let be a Banach space, and equip the space with uniform topology Von Neumann algebrae, basic constructions von Neumann algebra A von Neumann algebra is a subalgebra which is closed under the weak operator topology. Von Neumann bicommutant theorem