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- Doctoral Dissertations [1438]

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Title | Sequence spaces and the basis concept in Banach spaces |
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Author | Harvey, James Ronald |

Date | 1969 |

Genre | Dissertation |

Degree | Doctor of Philosophy |

Abstract | A sequence of vectors, (x_n), in a Banach space E is a basis for E if there exists a sequence (X_n) of linear functionals on E such that the following conditions hold; (i)x = Summation of X_n(x)x_n for all x in E, (ii) X_n is continuous for each n, (iii) (x_n) is biorthogonal to (X_n). If (x_n) is any sequence of non-zero vectors in E then S = {(a_n) : Summation of a_n x_n converges in E} is a Banach space. This dissertation investigates the properties of S that imply the existence of linear functionals on E such that one or more of the above conditions hold. |

Link | https://repository.tcu.edu/handle/116099117/33804 |

Department | Mathematics |

Advisor | Sanders, Bobby L. |

- Doctoral Dissertations [1438]

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