This HTML5 document contains 100 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dbpedia-dehttp://de.dbpedia.org/resource/
dctermshttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n17https://global.dbpedia.org/id/
yagohttp://dbpedia.org/class/yago/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
dbpedia-plhttp://pl.dbpedia.org/resource/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
provhttp://www.w3.org/ns/prov#
dbchttp://dbpedia.org/resource/Category:
dbphttp://dbpedia.org/property/
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/
dbpedia-jahttp://ja.dbpedia.org/resource/

Statements

Subject Item
dbr:List_of_functional_analysis_topics
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Metrizable_space
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:System_of_imprimitivity
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Partial_trace
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Representation_theory_of_the_Lorentz_group
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Von_Neumann_bicommutant_theorem
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Real_analysis
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Von_Neumann_algebra
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Uniformly_bounded_representation
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Glossary_of_representation_theory
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Operator_topologies
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Oscillator_representation
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Locally_convex_topological_vector_space
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Bochner's_theorem
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Singular_integral_operators_of_convolution_type
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Commutation_theorem_for_traces
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Compact_operator_on_Hilbert_space
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Kuiper's_theorem
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Stone's_theorem_on_one-parameter_unitary_groups
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Weak_topology
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Ergodic_flow
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Ergodic_theory
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Kaplansky_density_theorem
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Cotlar–Stein_lemma
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Singular_integral_operators_on_closed_curves
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Abstract_differential_equation
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Bicommutant
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:C0-semigroup
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Polish_space
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Spectral_theory_of_ordinary_differential_equations
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Sot
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
dbo:wikiPageDisambiguates
dbr:Strong_operator_topology
Subject Item
dbr:Strong_operator_topology
rdf:type
yago:Space100028651 yago:Attribute100024264 yago:WikicatBanachSpaces yago:WikicatTopologicalVectorSpaces yago:Abstraction100002137
rdfs:label
Strong operator topology Starke Operatortopologie 強作用素位相 Silna topologia operatorowa
rdfs:comment
数学の一分野である関数解析学における強作用素位相（きょうさようそいそう、英: strong operator topology; SOT）とは、ヒルベルト空間上の（あるいは、より一般にバナッハ空間上の）有界作用素全体の成す集合上の局所凸位相で、作用素 T を実数 へと写す評価写像がそのヒルベルト空間内の各ベクトル x について連続であるようなもののうち最弱のものを言う。 SOT は、弱作用素位相よりも、ノルム位相よりも弱い。 SOT は、弱作用素位相の備える良い性質をいくつか欠いているが、より強い位相であるため、この位相において様々な物事を証明することはしばしばより簡単なこととなる。さらにそれは自然なことで、なぜならば SOT は単純に作用素の点別収束の位相だからである。 ノルム位相がの枠組みを与えるように、SOT はの枠組みを与える。 ヒルベルト空間上の有界作用素からなる集合上の線型汎函数で、SOT において連続であるようなものは、WOT（弱作用素位相）においても連続である。このことより、WOT における作用素の凸集合の閉包は、SOT におけるそのような集合の閉包と等しい。 上述の用語は、ヒルベルト空間の作用素の収束の性質を言い換えるものであることにも注意されたい。特に、複素ヒルベルト空間に対しては、偏極公式により、強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。 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). Silna topologia operatorowa (mocna topologia operatorowa; także SOT od ang. strong operator topology) - dla pary przestrzeni Banacha E i F topologia lokalnie wypukła w przestrzeni B(E, F) wszystkich operatorów liniowych i ograniczonych z E do F wprowadzona przez rodzinę półnorm fx danych wzorami: gdzie x ∈ E. Silna topologia operatorowa jest więc niczym innym jak topologią zbieżności punktowej w B(E, F).
dcterms:subject
dbc:Banach_spaces dbc:Topology_of_function_spaces
dbo:wikiPageID
458699
dbo:wikiPageRevisionID
1108337301
dbo:wikiPageWikiLink
dbr:Topologies_on_the_set_of_operators_on_a_Hilbert_space dbr:Subbase dbr:Mathematics dbc:Banach_spaces dbr:Weak_operator_topology dbr:Bounded_operator dbr:Functional_analysis dbr:Finer_topology dbr:Strongly_continuous_semigroup dbr:Initial_topology dbr:Operator_norm dbc:Topology_of_function_spaces dbr:Linear_functional dbr:Topology dbr:Continuous_functional_calculus dbr:Measurable_functional_calculus dbr:Locally_convex_topological_vector_space dbr:Hilbert_space dbr:Convex_set
owl:sameAs
yago-res:Strong_operator_topology dbpedia-pl:Silna_topologia_operatorowa wikidata:Q4392013 n17:445Bn dbpedia-ja:強作用素位相 freebase:m.02bzhq dbpedia-de:Starke_Operatortopologie
dbp:wikiPageUsesTemplate
dbt:Banach_spaces dbt:Rudin_Walter_Functional_Analysis dbt:Duality_and_spaces_of_linear_maps dbt:Functional_analysis dbt:Cite_book dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Short_description dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels dbt:Hilbert_space dbt:Reflist dbt:Narici_Beckenstein_Topological_Vector_Spaces
dbo:abstract
数学の一分野である関数解析学における強作用素位相（きょうさようそいそう、英: strong operator topology; SOT）とは、ヒルベルト空間上の（あるいは、より一般にバナッハ空間上の）有界作用素全体の成す集合上の局所凸位相で、作用素 T を実数 へと写す評価写像がそのヒルベルト空間内の各ベクトル x について連続であるようなもののうち最弱のものを言う。 SOT は、弱作用素位相よりも、ノルム位相よりも弱い。 SOT は、弱作用素位相の備える良い性質をいくつか欠いているが、より強い位相であるため、この位相において様々な物事を証明することはしばしばより簡単なこととなる。さらにそれは自然なことで、なぜならば SOT は単純に作用素の点別収束の位相だからである。 ノルム位相がの枠組みを与えるように、SOT はの枠組みを与える。 ヒルベルト空間上の有界作用素からなる集合上の線型汎函数で、SOT において連続であるようなものは、WOT（弱作用素位相）においても連続である。このことより、WOT における作用素の凸集合の閉包は、SOT におけるそのような集合の閉包と等しい。 上述の用語は、ヒルベルト空間の作用素の収束の性質を言い換えるものであることにも注意されたい。特に、複素ヒルベルト空間に対しては、偏極公式により、強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。 Silna topologia operatorowa (mocna topologia operatorowa; także SOT od ang. strong operator topology) - dla pary przestrzeni Banacha E i F topologia lokalnie wypukła w przestrzeni B(E, F) wszystkich operatorów liniowych i ograniczonych z E do F wprowadzona przez rodzinę półnorm fx danych wzorami: gdzie x ∈ E. Silna topologia operatorowa jest więc niczym innym jak topologią zbieżności punktowej w B(E, F). 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). In concrete terms, this means that in the strong operator topology if and only if for each x in H. 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 can be viewed as more natural, too, since it is simply the topology of pointwise convergence. 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 weak operator topology (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. This language translates into convergence properties of Hilbert space operators. For a complex Hilbert space, it is easy to verify by the polarization identity, that Strong Operator convergence implies Weak Operator convergence.
prov:wasDerivedFrom
wikipedia-en:Strong_operator_topology?oldid=1108337301&ns=0
dbo:wikiPageLength
2986
foaf:isPrimaryTopicOf
wikipedia-en:Strong_operator_topology
Subject Item
dbr:Walsh_function
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Weak_operator_topology
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:List_of_topologies
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Peter–Weyl_theorem
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Strong_topology
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Strong_convergence
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
Subject Item
dbr:Strongly_continuous_family_of_operators
dbo:wikiPageWikiLink
dbr:Strong_operator_topology
dbo:wikiPageRedirects
dbr:Strong_operator_topology
Subject Item
wikipedia-en:Strong_operator_topology
foaf:primaryTopic
dbr:Strong_operator_topology