Solved Problems—Normed Spaces and Inner Product Spaces

Consider the vector space V of real polynomials of degree less than or equal to n. Fix distinct real numbers \(a_0,a_1, \ldots , a_k\) . For \(p \in V\) , \(max \lbrace |p(a_j) |: 0 \le j \le k \rbrace \) defines a norm on V.