Category:Evaluation Linear Transformations (Normed Vector Spaces)
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This category contains results about evaluation linear transformations in the context of normed vector spaces.
Let $\Bbb F \in \set {\R, \C}$.
Let $\struct {X, \norm \cdot_X}$ be a normed vector space over $\Bbb F$.
Let $\struct {X^\ast, \norm \cdot_{X^\ast} }$ be the normed dual of $\struct {X, \norm \cdot_X}$.
Let $\struct {X^{\ast \ast}, \norm \cdot_{X^{\ast \ast} } }$ be the second normed dual of $\struct {X, \norm \cdot_X}$.
For each $x \in X$, define $x^\wedge : X^\ast \to \Bbb F$ by:
- $\map {x^\wedge} f = \map f x$
Then we define the evaluation linear transformation from $X$ into $X^{\ast \ast}$ as the function $\iota : X \to X^{\ast \ast}$ defined by:
- $\map \iota x = x^\wedge$
for each $x \in X$.
Pages in category "Evaluation Linear Transformations (Normed Vector Spaces)"
The following 6 pages are in this category, out of 6 total.
E
- Evaluation Linear Transformation on Normed Vector Space is Linear Isometry
- Evaluation Linear Transformation on Normed Vector Space is Linear Transformation from Space to Second Normed Dual
- Evaluation Linear Transformation on Normed Vector Space is Weak to Weak-* Continuous Embedding into Second Normed Dual