 Solution

ID: past-exam-of-the-functional-analysis-course-of-the-university-of-oxford/2011/3/i/solution

A biorthogonal system is a family

(x_{i}, f_{i})_{i \in I}

with

x_{i} \in X

f_{i} \in X^{*}

, satisfying

f_{i} (x_{j}) = δ_{ij} (i, j \in I) .

Thus each continuous coordinate functional takes value one on its own vector and zero on all others. The vectors need not be orthogonal in any inner product, and totality of their linear span is an additional condition.

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