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- Sequence_space abstract "In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space.The most important sequences spaces in analysis are the ℓp spaces, consisting of the p-power summable sequences, with the p-norm. These are special cases of Lp spaces for the counting measure on the set of natural numbers. Other important classes of sequences like convergent sequences or null sequences form sequence spaces, respectively denoted c and c0, with the sup norm. Any sequence space can also be equipped with the topology of pointwise convergence, under which it becomes a special kind of Fréchet space called FK-space.".
- Sequence_space wikiPageID "1701075".
- Sequence_space wikiPageRevisionID "605968648".
- Sequence_space hasPhotoCollection Sequence_space.
- Sequence_space subject Category:Functional_analysis.
- Sequence_space subject Category:Sequence_spaces.
- Sequence_space subject Category:Sequences_and_series.
- Sequence_space type Abstraction100002137.
- Sequence_space type Arrangement107938773.
- Sequence_space type Attribute100024264.
- Sequence_space type Group100031264.
- Sequence_space type Ordering108456993.
- Sequence_space type Sequence108459252.
- Sequence_space type SequenceSpaces.
- Sequence_space type SequencesAndSeries.
- Sequence_space type Series108457976.
- Sequence_space type Space100028651.
- Sequence_space comment "In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers.".
- Sequence_space label "Espace de suites ℓp".
- Sequence_space label "Espaço lp".
- Sequence_space label "Folgenraum".
- Sequence_space label "Sequence space".
- Sequence_space label "Spazio delle successioni".
- Sequence_space label "数列空間".
- Sequence_space sameAs Folgenraum.
- Sequence_space sameAs Espace_de_suites_ℓp.
- Sequence_space sameAs Spazio_delle_successioni.
- Sequence_space sameAs 数列空間.
- Sequence_space sameAs Espaço_lp.
- Sequence_space sameAs m.05phst.
- Sequence_space sameAs Q289411.
- Sequence_space sameAs Q289411.
- Sequence_space sameAs Sequence_space.
- Sequence_space wasDerivedFrom Sequence_space?oldid=605968648.
- Sequence_space isPrimaryTopicOf Sequence_space.