Definition:Support Functional
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Definition
Let $\struct {X, \norm \cdot_X}$ be a normed vector space.
Let $\struct {X^\ast, \norm \cdot_{X^\ast} }$ be the normed dual space of $X$.
Let $x \in X$.
We say that $f \in X^\ast$ is a support functional at $x$ if and only if:
- $(1): \quad$ $\norm f_{X^\ast} = 1$
- $(2): \quad$ $\map f x = \norm x_X$.
Also see
Sources
- 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $20.1$: Existence of a Support Functional