journal6 ›› 2006, Vol. 27 ›› Issue (2): 25-27.

• Mathematics • Previous Articles     Next Articles

Complete Space and Conjugate Space of a Normed Space


  1. (1.Editorial Board of Journal of Jishou University,Jishou 416000,Hunan China;2.Department of Mathematics,Capital Normal University,Beijing 100037,China;3.College of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China)
  • Online:2006-03-25 Published:2012-09-16

Abstract: It is proved that the normed linear space R∞ imcomplete,R∞={(an)|an∈R,{an} being a real bounded sequence,‖(an)‖=supn≥1 λn|an|}.Its complete space are conjugate space are given,and the sufficient or necessary conditions are obtained for a linear operator from R∞ to R∞ to be continuous.

Key words: Banach space, conjugate space, continuous linear operator

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