Infinite Dimensional Vector Spaces and Linear Operators
Give a example where V is an infinite dimensional vector space , are linear operators on V and (a composition) is a bijection but T_1 and T_2 are not bijections
Give a example where V is an infinite dimensional vector space , are linear operators on V and (a composition) is a bijection but T_1 and T_2 are not bijections
Think of the space and don't think too hard about the mappings...do what's natural.
The real vector space whose elements are the polynomials with real coefficients on the unknown considering the standard operation sum an product by a real number.
Give a example where V is an infinite dimensional vector space , are linear operators on V and (a composition) is a bijection but T_1 and T_2 are not bijections
Take the vector space of all
real sequences with coordinatewise addition and multiplication by scalar, and take