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- Strong_operator_topology abstract "In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest locally convex topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map sending an operator T to the real number is continuous for each vector x in the Hilbert space.The SOT is stronger than the weak operator topology and weaker than the norm topology.The SOT lacks some of the nicer properties that the weak operator topology has, but being stronger, things are sometimes easier to prove in this topology. It is more natural too, since it is simply the topology of pointwise convergence for an operator. The SOT topology also provides the framework for the measurable functional calculus, just as the norm topology does for the continuous functional calculus. The linear functionals on the set of bounded operators on a Hilbert space that are continuous in the SOT are precisely those continuous in the WOT. Because of this, the closure of a convex set of operators in the WOT is the same as the closure of that set in the SOT.It should also be noted that the above language translates into convergence properties of Hilbert space operators. One especially observes that for a complex Hilbert space, by way of the polarization identity, one easily verifies that Strong Operator convergence implies Weak Operator convergence.".
- Strong_operator_topology wikiPageID "458699".
- Strong_operator_topology wikiPageRevisionID "605908392".
- Strong_operator_topology hasPhotoCollection Strong_operator_topology.
- Strong_operator_topology subject Category:Topology_of_function_spaces.
- Strong_operator_topology comment "In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest locally convex topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map sending an operator T to the real number is continuous for each vector x in the Hilbert space.The SOT is stronger than the weak operator topology and weaker than the norm topology.The SOT lacks some of the nicer properties that the weak operator topology has, but being stronger, things are sometimes easier to prove in this topology. ".
- Strong_operator_topology label "Silna topologia operatorowa".
- Strong_operator_topology label "Strong operator topology".
- Strong_operator_topology label "強作用素位相".
- Strong_operator_topology sameAs 強作用素位相.
- Strong_operator_topology sameAs Silna_topologia_operatorowa.
- Strong_operator_topology sameAs m.02bzhq.
- Strong_operator_topology sameAs Q4392013.
- Strong_operator_topology sameAs Q4392013.
- Strong_operator_topology wasDerivedFrom Strong_operator_topology?oldid=605908392.
- Strong_operator_topology isPrimaryTopicOf Strong_operator_topology.