C space (original) (raw)
함수해석학에서 수렴 수열 공간(收斂數列空間, 영어: space of convergent sequence)은 어떤 값으로 수렴하는 수열들로 구성된 바나흐 공간이다. 기호는 c.
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| dbo:abstract | In the mathematical field of functional analysis, the space denoted by c is the vector space of all convergent sequences of real numbers or complex numbers. When equipped with the uniform norm: the space becomes a Banach space. It is a closed linear subspace of the space of bounded sequences, , and contains as a closed subspace the Banach space of sequences converging to zero. The dual of is isometrically isomorphic to as is that of In particular, neither nor is reflexive. In the first case, the isomorphism of with is given as follows. If then the pairing with an element in is given by This is the Riesz representation theorem on the ordinal For the pairing between in and in is given by (en) 함수해석학에서 수렴 수열 공간(收斂數列空間, 영어: space of convergent sequence)은 어떤 값으로 수렴하는 수열들로 구성된 바나흐 공간이다. 기호는 c. (ko) 数学の分野、函数解析学において実または複素の (xn) 全体からなるベクトル空間は c と書かれる。これに一様ノルム を考えるとき、収束数列の空間 c はバナッハ空間を成す。これは有界数列の空間 ℓ∞ の閉部分空間であり、かつまたの（バナッハ）空間 c0 を閉部分空間として含む。c の双対空間は（c0 のと同じく）ℓ1 に等長同型である。特に c と c0 の何れも回帰的でない。前者について、ℓ1 と c* が同型であることは内積を、(x0,x1,...) ∈ ℓ1 と (y1,y2,...) ∈ c に対して と与えればよい。これは順序数 ω 上で考えたリースの表現定理である。他方 c0 について、(xi) ∈ ℓ1 と (yi) ∈ c0 の内積は とすればよい。 (ja) |
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| dbo:wikiPageWikiLink | dbc:Banach_spaces dbr:Riesz_representation_theorem dbr:Uniform_norm dbr:Vector_space dbr:Complex_number dbr:Mathematics dbr:Lp_space dbr:Closed_set dbr:Functional_analysis dbr:Banach_space dbr:Linear_subspace dbr:Dual_space dbc:Normed_spaces dbc:Functional_analysis dbc:Norms_(mathematics) dbr:Real_number dbr:Reflexive_space dbr:Ordinal_(mathematics) dbr:Convergent_sequence dbr:Space_of_bounded_sequences |
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| rdf:type | yago:WikicatBanachSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:Space100028651 |
| rdfs:comment | 함수해석학에서 수렴 수열 공간(收斂數列空間, 영어: space of convergent sequence)은 어떤 값으로 수렴하는 수열들로 구성된 바나흐 공간이다. 기호는 c. (ko) 数学の分野、函数解析学において実または複素の (xn) 全体からなるベクトル空間は c と書かれる。これに一様ノルム を考えるとき、収束数列の空間 c はバナッハ空間を成す。これは有界数列の空間 ℓ∞ の閉部分空間であり、かつまたの（バナッハ）空間 c0 を閉部分空間として含む。c の双対空間は（c0 のと同じく）ℓ1 に等長同型である。特に c と c0 の何れも回帰的でない。前者について、ℓ1 と c* が同型であることは内積を、(x0,x1,...) ∈ ℓ1 と (y1,y2,...) ∈ c に対して と与えればよい。これは順序数 ω 上で考えたリースの表現定理である。他方 c0 について、(xi) ∈ ℓ1 と (yi) ∈ c0 の内積は とすればよい。 (ja) In the mathematical field of functional analysis, the space denoted by c is the vector space of all convergent sequences of real numbers or complex numbers. When equipped with the uniform norm: the space becomes a Banach space. It is a closed linear subspace of the space of bounded sequences, , and contains as a closed subspace the Banach space of sequences converging to zero. The dual of is isometrically isomorphic to as is that of In particular, neither nor is reflexive. This is the Riesz representation theorem on the ordinal For the pairing between in and in is given by (en) |
| rdfs:label | C space (en) 수렴 수열 공간 (ko) 収束数列空間 (ja) |
| owl:sameAs | freebase:C space wikidata:C space dbpedia-ja:C space dbpedia-ko:C space https://global.dbpedia.org/id/4e8gU yago-res:C space |
| prov:wasDerivedFrom | wikipedia-en:C_space?oldid=1081143946&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:C_space |
| is dbo:wikiPageDisambiguates of | dbr:C_(disambiguation) |
| is dbo:wikiPageWikiLink of | dbr:Bs_space dbr:Sequence_space dbr:C_(disambiguation) |
| is rdfs:seeAlso of | dbr:Sequence_space |
| is foaf:primaryTopic of | wikipedia-en:C_space |