Question

Show that the space L²(R) of all square of summable real sequence is a linear space over a vector field R

Answer 1

sequences satisfy properties of linear space:

addition: $\{x_n+y_n\}=\{x_n\}+\{y_n\}$

scalar multiplication: $\{ax_n\}=a\{x_n\}$

So, the space L²(R) of all square of summable real sequence is a linear space over a vector field R.