Unbounded linear operator

**raed** · March 29th 2011, 11:23 PM

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.

**girdav** · March 30th 2011, 09:41 AM

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.

Thread: Unbounded linear operator

LinkBack

Thread Tools

Display

Unbounded linear operator

Similar Math Help Forum Discussions

Linear operator

The adjoint of unbounded operator

Is this Linear Operator?

linear operator

linear operator

Search Tags