Definition:Vector Space of Sequences with Finite Support
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Definition
Let $\struct {K, +, \circ}$ be a division ring.
Let $K^\N$ be the set of sequences $\sequence{ a_n }_{n \in \N}$ in $K$.
Regard $K^\N$ as a vector space of all mappings from $\N$ to $K$.
The vector space of sequences with finite support is the vector subspace of $K^\N$ of sequences with finite support:
- $\ds \set{ f \in K^\N: \text{$f$ has finite support} }$
There is no standard symbol for the vector space of sequences with finite support.
Also see
Sources
- 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next): $\text{I}$ Hilbert Spaces: $\S 1.$ Elementary Properties and Examples: Example $1.2$