Strong operator topology
In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced by the seminorms of the form , as x varies in H. Equivalently, it is the coarsest topology such that, for each fixed x in H, the evaluation map (taking values in H) is continuous in T. The equivalence of these two definitions can be seen by observing that a subbase for both topologies is given by the sets (where T0 is any bounded operator on H, x is any vector and ε is any positive real number).
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Strong operator topology
In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced by the seminorms of the form , as x varies in H. Equivalently, it is the coarsest topology such that, for each fixed x in H, the evaluation map (taking values in H) is continuous in T. The equivalence of these two definitions can be seen by observing that a subbase for both topologies is given by the sets (where T0 is any bounded operator on H, x is any vector and ε is any positive real number).
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In functional analysis, a bran ...... ies Weak Operator convergence.
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Silna topologia operatorowa (m ...... bieżności punktowej w B(E, F).
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数学の一分野である関数解析学における強作用素位相(きょうさよ ...... 作用素収束は弱作用素収束を含意することが容易に確かめられる。
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In functional analysis, a bran ...... is any positive real number).
@en
Silna topologia operatorowa (m ...... bieżności punktowej w B(E, F).
@pl
数学の一分野である関数解析学における強作用素位相(きょうさよ ...... 作用素収束は弱作用素収束を含意することが容易に確かめられる。
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Silna topologia operatorowa
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Starke Operatortopologie
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Strong operator topology
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強作用素位相
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