# Category:Evaluation Linear Transformations (Normed Vector Spaces)

Jump to navigation
Jump to search

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