This one probably isn't that hard, though right now I'm having some trouble.
Suppose is a vector space over a field .
Let be the right shift operator and be the left shift operator (both as defined below).
Before I go further, I'll need to provide a definition of the right/left shift operators.
Let be the space of infinite row vectors
is the zero space; is a proper subspace of
is a proper subspace of ; is the whole space.
a) Prove that is linear.
b) Prove that
c) Prove that is not invertible.
This probably isn't that difficult, and I'm just looking at it the wrong way.