![PDF) On convexity, smoothness and renormings in the study of faces of the unit ball of a Banach space | Francisco J Garcia-Pacheco - Academia.edu PDF) On convexity, smoothness and renormings in the study of faces of the unit ball of a Banach space | Francisco J Garcia-Pacheco - Academia.edu](https://0.academia-photos.com/attachment_thumbnails/42396281/mini_magick20190217-7239-2mn8cm.png?1550457897)
PDF) On convexity, smoothness and renormings in the study of faces of the unit ball of a Banach space | Francisco J Garcia-Pacheco - Academia.edu
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![SOLVED: Consider the unidirectional set C[-1,1] defined by @(x) = (h(x),d(x),c(x)) for x in C[-1,1]. Show that for all x in the closed unit ball of C[-1,1], it fails to be reflexive. SOLVED: Consider the unidirectional set C[-1,1] defined by @(x) = (h(x),d(x),c(x)) for x in C[-1,1]. Show that for all x in the closed unit ball of C[-1,1], it fails to be reflexive.](https://cdn.numerade.com/ask_images/f01b5543732b405f8f70237961157c1c.jpg)
SOLVED: Consider the unidirectional set C[-1,1] defined by @(x) = (h(x),d(x),c(x)) for x in C[-1,1]. Show that for all x in the closed unit ball of C[-1,1], it fails to be reflexive.
![SOLVED: Show that the closed unit ball in a Hilbert space H is compact if and only if H is finite dimensional. HINT: The closed unit ball must contain any basis. SOLVED: Show that the closed unit ball in a Hilbert space H is compact if and only if H is finite dimensional. HINT: The closed unit ball must contain any basis.](https://cdn.numerade.com/project-universal/previews/507d7996-b134-4813-ac60-98bfcdcf3d67.gif)
SOLVED: Show that the closed unit ball in a Hilbert space H is compact if and only if H is finite dimensional. HINT: The closed unit ball must contain any basis.
![real analysis - Will the "closed" unit ball $\left\| x \right\| \le 1$ in $\Bbb R^n$ be a compact set for any norm? - Mathematics Stack Exchange real analysis - Will the "closed" unit ball $\left\| x \right\| \le 1$ in $\Bbb R^n$ be a compact set for any norm? - Mathematics Stack Exchange](https://i.stack.imgur.com/MD2uR.png)
real analysis - Will the "closed" unit ball $\left\| x \right\| \le 1$ in $\Bbb R^n$ be a compact set for any norm? - Mathematics Stack Exchange
![functional analysis - Can we visualize the closed balls for the space $l^{\infty}$ equipped with the $\sup$ norm - Mathematics Stack Exchange functional analysis - Can we visualize the closed balls for the space $l^{\infty}$ equipped with the $\sup$ norm - Mathematics Stack Exchange](https://i.stack.imgur.com/StSEn.jpg)
functional analysis - Can we visualize the closed balls for the space $l^{\infty}$ equipped with the $\sup$ norm - Mathematics Stack Exchange
![SOLVED: Let B denote the closed unit ball in R³: B = (x, y, z) ∈ R³: x² + y² + z² < 1 Let f: R³ â†' R be the function SOLVED: Let B denote the closed unit ball in R³: B = (x, y, z) ∈ R³: x² + y² + z² < 1 Let f: R³ â†' R be the function](https://cdn.numerade.com/ask_images/6655d28922654ca6acfbbec454651857.jpg)
SOLVED: Let B denote the closed unit ball in R³: B = (x, y, z) ∈ R³: x² + y² + z² < 1 Let f: R³ â†' R be the function
![real analysis - Show that S is non-compact and deduce further that the closed unit ball in X is non-compact. - Mathematics Stack Exchange real analysis - Show that S is non-compact and deduce further that the closed unit ball in X is non-compact. - Mathematics Stack Exchange](https://i.stack.imgur.com/BOYPV.png)