Question

Showing that inf$_{x \in M}||x||_{E} = \frac{1}{||f||}$ for $E$ a Banach space, $f \in E'$ and $M = \{x \in E: f(x) =1\}$

score 126 · Answer 1 · 2018-03-12 12:19:47

126

Views

Showing that inf$_{x \in M}||x||_{E} = \frac{1}{||f||}$ for $E$ a Banach space, $f \in E'$ and $M = \{x \in E: f(x) =1\}$

Published on 12 Mar 2018 - 12:19

score 2.5k · Answer 2 · 2018-03-13 16:36:23

2.5k

Views

Convergence of infinite product to zero implies series divergence

Published on 13 Mar 2018 - 16:36

score 76 · Answer 3 · 2018-03-15 04:00:17

76

Views

proof by contradiction (clarification)

Published on 15 Mar 2018 - 4:00

score 118 · Answer 4 · 2026-03-25 03:20:42

118

Views

On finding $\sup\left\{3(-1)^n-\frac{1}{n^2+1}\right\}$

Published on 25 Mar 2026 - 3:20

score 71 · Answer 5 · 2018-03-15 20:23:11

71

Views

If $g(x) = \sup_{z \in [x, b]} f(z)$ is a concave function then $f(x)$ is also concave

Published on 15 Mar 2018 - 20:23

score 1.4k · Answer 6 · 2026-03-25 09:46:30

1.4k

Views

Problem about Riemann lower sum in piecewise-defined function

Published on 25 Mar 2026 - 9:46

score 50 · Answer 7 · 2018-03-18 06:33:23

50

Views

The infimum of the given set

Published on 18 Mar 2018 - 6:33

score 313 · Answer 8 · 2018-03-19 13:59:33

313

Views

Showing that a linear map does not achieve its norm

Published on 19 Mar 2018 - 13:59

score 33 · Answer 9 · 2018-03-19 18:02:42

33

Views

Exists an $h$ such that $\lVert u + hv \rVert_{\infty}= \max_{x \in U}|u(x)+hv(x)|$

Published on 19 Mar 2018 - 18:02

score 2.9k · Answer 10 · 2018-03-22 18:01:58

2.9k

Views

How can a finite set not have a maximum or minimum?

Published on 22 Mar 2018 - 18:01

score 29 · Answer 11 · 2018-03-25 21:12:28

29

Views

Showing that $\inf(r,s)=r\;\;\forall\;\;r,s\in \Re\;\;\text{and}\;\;s> r$

Published on 25 Mar 2018 - 21:12

score 406 · Answer 12 · 2018-03-26 11:03:38

406

Views

Let $f$ be a function with the IVP and for a fix $y$ let $M$ be $\{x\in\mathbb R\mid f(x)=y\}$. If $M$ is non-empty and bounded, then $\sup M\in M$.

Published on 26 Mar 2018 - 11:03

score 225 · Answer 13 · 2018-03-26 12:14:15

225

Views

A function with $\lim_{x \to \pm \infty} f(f(x))=\pm \infty$

Published on 26 Mar 2018 - 12:14

score 56 · Answer 14 · 2018-03-26 14:47:36

56

Views

Proof verification - Infimum

Published on 26 Mar 2018 - 14:47

score 98 · Answer 15 · 2018-03-26 23:24:32

98

Views

Infinitely many elements?

Published on 26 Mar 2018 - 23:24

List Question

Showing that inf$_{x \in M}||x||_{E} = \frac{1}{||f||}$ for $E$ a Banach space, $f \in E'$ and $M = \{x \in E: f(x) =1\}$

Convergence of infinite product to zero implies series divergence

proof by contradiction (clarification)

On finding $\sup\left\{3(-1)^n-\frac{1}{n^2+1}\right\}$

If $g(x) = \sup_{z \in [x, b]} f(z)$ is a concave function then $f(x)$ is also concave

Problem about Riemann lower sum in piecewise-defined function

The infimum of the given set

Showing that a linear map does not achieve its norm

Exists an $h$ such that $\lVert u + hv \rVert_{\infty}= \max_{x \in U}|u(x)+hv(x)|$

How can a finite set not have a maximum or minimum?

Showing that $\inf(r,s)=r\;\;\forall\;\;r,s\in \Re\;\;\text{and}\;\;s> r$

Let $f$ be a function with the IVP and for a fix $y$ let $M$ be $\{x\in\mathbb R\mid f(x)=y\}$. If $M$ is non-empty and bounded, then $\sup M\in M$.

A function with $\lim_{x \to \pm \infty} f(f(x))=\pm \infty$

Proof verification - Infimum

Infinitely many elements?

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