Results 1 to 2 of 2

Math Help - Unbounded linear operator

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    164

    Unbounded linear operator

    Dear Colleagues,

    Could you please help me in solving the following problem:
    Let X and Y\neq \{0\} be normed spaces, where dimX=\infty. Show that there is at least one unbounded linear operator T:X\longrightarrow Y.

    Regards,

    Raed.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32
    Let (e_i)_{i\in I} a Hamel basis for X. Let \left\{ f_n\right\} a sequence of linearly independent vectors of that basis. Let v\neq 0\in Y. Put T(f_n) = n\lVert f_n\rVert v and T(e_i) =0 if e_i is not one of the f_n. You can show that T is linear and not bounded.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear operator
    Posted in the Differential Geometry Forum
    Replies: 11
    Last Post: June 5th 2011, 11:41 PM
  2. The adjoint of unbounded operator
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 22nd 2010, 11:32 AM
  3. Is this Linear Operator?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 14th 2010, 02:59 PM
  4. linear operator
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 16th 2008, 06:12 PM
  5. linear operator
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 13th 2008, 09:24 PM

Search Tags


/mathhelpforum @mathhelpforum