Sequence Spaces
- is a type of mathematical space
- is a linear subspace of the vector space of all sequences (𝐹ℕ)
- is a vector space (𝑉,𝐹) whose elements are (infinite?) sequences of real numbers or complex numbers
- equivalently, it is a function space whose elements are functions from the natural numbers (ℕ) to the field (𝐹) of real numbers or complex numbers
Sequence Spaces - Definition
A sequence space is any linear subspace of the vector space of all sequences (𝐹ℕ).
Sequence Spaces - Examples/Types
- vector space of all sequences (𝐹ℕ)
- c spaces - is a sequence space of convergent sequences
- c0 spaces - is a c space of sequences that converges to 0
- c00 spaces - is a c0 space of sequences that is eventually 0
- c0 spaces - is a c space of sequences that converges to 0
- 𝓁𝑝 spaces (sequence space)
- 𝐿𝑝 spaces (function space) 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 number
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