UNT Theses and Dissertations - 3 Matching Results

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Duals and Weak Completeness in Certain Sequence Spaces

Description: In this paper the weak completeness of certain sequence spaces is examined. In particular, we show that each of the sequence spaces c0 and 9, 1 < p < c, is a Banach space. A Riesz representation for the dual space of each of these sequence spaces is given. A Riesz representation theorem for Hilbert space is also proven. In the third chapter we conclude that any reflexive space is weakly (sequentially) complete. We give 01 as an example of a non-reflexive space that is weakly complete. Two examp… more
Date: August 1980
Creator: Leavelle, Tommy L. (Tommy Lee)
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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The Riesz Representation Theorem

Description: In 1909, F. Riesz succeeded in giving an integral represntation for continuous linear functionals on C[0,1]. Although other authors, notably Hadamard and Frechet, had given representations for continuous linear functionals on C[0,1], their results lacked the clarity, elegance, and some of the substance (uniqueness) of Riesz's theorem. Subsequently, the integral representation of continuous linear functionals has been known as the Riesz Representation Theorem. In this paper, three different pro… more
Date: August 1980
Creator: Williams, Stanley C. (Stanley Carl)
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Measurable Selection Theorems for Partitions of Polish Spaces into Gδ Equivalence Classes

Description: Let X be a Polish space and Q a measurable partition of X into Gδ equivalence classes. In 1978, S. M. Srivastava proved the existence of a Borel cross section for Q. He asked whether more can be concluded in case each equivalence class is uncountable. This question is answered here in the affirmative. The main result of the author is a proof that shows the existence of a Castaing Representation for Q.
Date: May 1980
Creator: Simrin, Harry S.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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