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BK-space

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In functional analysis and related areas of mathematics, a BK-space or Banach coordinate space is a sequence space endowed with a suitable norm to turn it into a Banach space. All BK-spaces are normable FK-spaces.[1]

Examples

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The space of convergent sequences the space of vanishing sequences and the space of bounded sequences under the supremum norm [1]

The space of absolutely p-summable sequences with and the norm [1]

See also

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  • FK-AK space
  • FK-space – Sequence space that is Fréchet
  • Normed space – Vector space on which a distance is defined
  • Sequence space – Vector space of infinite sequences

References

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  1. ^ a b c Banas, Jozef; Mursaleen, M. (2014), Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, p. 20, ISBN 9788132218869.