Operator Topology
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H.There are many topologies that can be defined on B(H) besides the ones used above. These topologies are all locally convex, which implies that they are defined by a family of seminorms. In analysis, a topology is called strong if it has many open sets and weak if it has few open sets, so that the co...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(H) of bounded linear operators on a Hilbert space H.There are many topologies that can be defined on B(H) besides the ones used above. These topologies are all locally convex, which implies that they are defined by a family of seminorms. In analysis, a topology is called strong if it has many open sets and weak if it has few open sets, so that the corresponding modes of convergence are, respectively, strong and weak. (In topology proper, these terms can suggest the opposite meaning, so strong and weak are replaced with, respectively, fine and coarse.) The diagram on the right is a summary of the relations, with the arrows pointing from strong to weak.
