Title page for etd-0623105-210702


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URN etd-0623105-210702
Author Shao-hua Yan
Author's Email Address m921020001@student.nsysu.edu.tw
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Department Applied Mathematics
Year 2004
Semester 2
Degree Master
Type of Document
Language English
Title Biseparating linear maps of continuous or smooth functions
Date of Defense 2005-06-10
Page Count 23
Keyword
  • biseparating linear maps
  • smooth function
  • continuous function
  • Abstract Let X. Y be compact Hausdorff spaces, and E, F be Banach spaces. A linear map T:C (X,E)→C (Y,F) is separating if ∥Tf(y)∥∥Tg(y)∥=0 whenever ∥f(x)∥∥g(x)∥=0, for every x belonging to X, y belonging to Y. Gau, Jeang and Wong prove that a biseparating linear bijection T is a weighted composition oprator Tf=hf○φ where h is a function from Y into the set of inveritable linear operators from E onto F and φ is a homeomorphism from Y onto X. In this thesis, we extend this result to the case that continuous functions are defined to a locally compact Hausdorff space, which is either σ-compact or first countable. Moreover, we give a short proof of a recent result of Mrcun. Finally, we give an alternative approach to an Araujo's result concerning biseparating maps of smooth functions appeared in Adv. Math.
    Advisory Committee
  • Mark C. Ho - chair
  • Hwa-Long Gau - co-chair
  • Ngai-Ching Wong - advisor
  • Files
  • etd-0623105-210702.pdf
  • indicate access worldwide
    Date of Submission 2005-06-23

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