Results 1 to 2 of 2

Math Help - Norm on dual space

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    18

    Norm on dual space

    If X is the space of ordered n-tuples of real numbers and ||x||=max|{\xi}_{j}| where x = ({\xi}_{1 }.......,{\xi}_{n}) , what is the corresponding norm on the dual space X'?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    675
    Thanks
    32
    x'\in X' can be represented by (a_1,\ldots,a_n)\in\mathbb{R}^n (we have \langle x',x\rangle  =\sum_{j=1}^na_jx_j). We have \lVert x'\rVert=\sup_{\lVert x'\rVert =1} \left|\langle x',x\rangle\right| and taking x_j = \mathrm{sgn}a_j we find \lVert x'\rVert  =\sum_{j=1}^n|a_j|.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Normed space and dual space
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: June 5th 2011, 10:46 PM
  2. Dual Space of a Vector Space Question
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 16th 2011, 03:02 AM
  3. Dual space of a vector space.
    Posted in the Advanced Algebra Forum
    Replies: 15
    Last Post: March 6th 2011, 02:20 PM
  4. vector space and its dual space
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 26th 2009, 08:34 AM
  5. Dual Space
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 31st 2007, 07:57 PM

Search Tags


/mathhelpforum @mathhelpforum