About: Unbounded operator

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In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since In contrast to bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain.

Attributes	Values
rdf:type	Thing yago:Operator113786413 yago:Relation100031921 yago:WikicatLinearOperators yago:Abstraction100002137 yago:Function113783816 yago:LinearOperator113786595 yago:MathematicalRelation113783581
rdfs:label	Unbounded operator
rdfs:comment	In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since In contrast to bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain.
rdfs:seeAlso	Extensions of symmetric operators
foaf:isPrimaryTopicOf	wikipedia-en:Unbounded_operator
dct:subject	Operator theory Linear operators
Wikipage page ID	1422584(xsd:integer)
Wikipage revision ID	970728426(xsd:integer)
Link from a Wikipage to another Wikipage	Unbounded operator Operator theory Bounded operator Operator theory Derivative Graph of a function Providence, Rhode Island Hyperplane Subset Discontinuous linear map Banach space Linear operators Normal operator Spectrum (functional analysis) Von Neumann's theorem Cayley transform Limit of a sequence Linear map Axiom of choice Function (mathematics) Functional analysis Hahn–Banach theorem Interval (mathematics) Sequence Functional calculus Observable American Mathematical Society Transpose Dense set Densely defined operator Hellinger–Toeplitz theorem Self-adjoint operator Complete metric space Continuous function Stone–von Neumann theorem Differential operator Hilbert space John von Neumann Mathematics Direct sum of modules Marshall Harvey Stone Closed range theorem Closed set Time evolution Topological vector space Stone's theorem on one-parameter unitary groups dbr:Smooth_function__''C''%3Csup%3E∞%3C/sup%3E(_%5B''a'',_''b''%5D_)
Link from a Wikipage to an external page	https://www.mat.univie.ac.at/~gerald/ftp/book-schroe/
sameAs	Unbounded operator Unbounded operator Unbounded operator
dbp:wikiPageUsesTemplate	dbt:! dbt:!! dbt:= dbt:Citation dbt:Citation_needed dbt:Cite_book dbt:Clarify dbt:Main dbt:Math dbt:Mvar dbt:Overline dbt:Reflist dbt:See_also dbt:Sfrac dbt:SpectralTheory dbt:Functional_Analysis dbt:PlanetMath_attribution dbt:Springer dbt:BoundednessAndBornology
date	May 2015
id	4526(xsd:integer) p/u095090
reason	This restriction is not adhered to in the article. Why the shift from Banach spaces to topological vector spaces? What is a bounded operator between topological vector spaces?
title	Closed operator Unbounded operator
has abstract	In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since * "unbounded" should sometimes be understood as "not necessarily bounded"; * "operator" should be understood as "linear operator" (as in the case of "bounded operator"); * the domain of the operator is a linear subspace, not necessarily the whole space; * this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense; * in the special case of a bounded operator, still, the domain is usually assumed to be the whole space. In contrast to bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain. The term "operator" often means "bounded linear operator", but in the context of this article it means "unbounded operator", with the reservations made above. The given space is assumed to be a Hilbert space. Some generalizations to Banach spaces and more general topological vector spaces are possible.
Link from a Wikipa... related subject.	dbpedia-de:Linearer_Operator
prov:wasDerivedFrom	wikipedia-en:Unbounded_operator?oldid=970728426&ns=0
page length (characters) of wiki page	33529(xsd:integer)
is rdfs:seeAlso of	Closed graph
is foaf:primaryTopic of	wikipedia-en:Unbounded_operator
is Link from a Wikipage to another Wikipage of	Contraction (operator theory)

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