Question

Show that $C^1[a,b]$ with the uniform norm is not a Banach space

score 385 · Answer 1 · 2026-03-25 21:49:46

385

Views

Show that $C^1[a,b]$ with the uniform norm is not a Banach space

Published on 25 Mar 2026 - 21:49

score 666 · Answer 2 · 2018-10-26 08:21:51

666

Views

Is it possibile to prove that a bounded sequence in a Lp normed space is Cauchy using the dominated convergence theorem?

Published on 26 Oct 2018 - 8:21

score 2.1k · Answer 3 · 2018-10-26 16:34:08

2.1k

Views

Prove that the space $C^k(\bar{U})$ is Banach.

Published on 26 Oct 2018 - 16:34

score 631 · Answer 4 · 2026-03-25 21:48:08

631

Views

How to show that $C_0 (U) $ is a Banach space

Published on 25 Mar 2026 - 21:48

score 55 · Answer 5 · 2018-10-28 02:51:39

55

Views

Computing $DF_{|_f}$ of $F(f)(x)=\int^{x}_{0}\cos\big(f^2(t)\big)dt,\text{ } x\in [0,1].$

Published on 28 Oct 2018 - 2:51

score 295 · Answer 6 · 2018-10-28 08:13:06

295

Views

Equicontinuity of the Image of a set of Functions under an Integral Operator.

Published on 28 Oct 2018 - 8:13

score 201 · Answer 7 · 2026-03-25 18:08:27

201

Views

Showing that $X=\{ f \in C[a,b] : f(a) = 0 \}$ is Banach

Published on 25 Mar 2026 - 18:08

score 104 · Answer 8 · 2018-10-28 19:30:10

104

Views

Show that $f_n \to f$ over $\| \cdot \|_\infty$ implies $f_n \to f$ over $\| \cdot \|_2$ and is $(C[a,b], \|\cdot\|_2)$ Banach?

Published on 28 Oct 2018 - 19:30

score 957 · Answer 9 · 2026-03-25 01:23:44

957

Views

$f = g$ almost everywhere implies $f =g$ for any continuous function $f$ and $g$.

Published on 25 Mar 2026 - 1:23

score 102 · Answer 10 · 2026-03-27 10:44:20

102

Views

An example for an operator with closed image but zero modulus

Published on 27 Mar 2026 - 10:44

score 40 · Answer 11 · 2018-10-29 11:50:04

40

Views

Density and codimension

Published on 29 Oct 2018 - 11:50

score 66 · Answer 12 · 2026-03-22 10:47:16

66

Views

There is a complemented subspace $E$ of $l^p$ such that $T$ is an isomorphism of $E$ onto a complemented subspace $T(E)$

Published on 22 Mar 2026 - 10:47

score 189 · Answer 13 · 2026-03-25 03:00:31

189

Views

A continuous Function from $R$ to a Banach Space is Borel-Measurable

Published on 25 Mar 2026 - 3:00

score 112 · Answer 14 · 2026-03-25 18:57:47

112

Views

Showing uniqueness of holomorphic functions on Banach spaces using uniquess of scalar holomorphic functions?

Published on 25 Mar 2026 - 18:57

score 44 · Answer 15 · 2018-11-02 04:14:33

44

Views

A question about norm of the bounded linear operator

Published on 02 Nov 2018 - 4:14

List Question

Show that $C^1[a,b]$ with the uniform norm is not a Banach space

Is it possibile to prove that a bounded sequence in a Lp normed space is Cauchy using the dominated convergence theorem?

Prove that the space $C^k(\bar{U})$ is Banach.

How to show that $C_0 (U) $ is a Banach space

Computing $DF_{|_f}$ of $F(f)(x)=\int^{x}_{0}\cos\big(f^2(t)\big)dt,\text{ } x\in [0,1].$

Equicontinuity of the Image of a set of Functions under an Integral Operator.

Showing that $X=\{ f \in C[a,b] : f(a) = 0 \}$ is Banach

Show that $f_n \to f$ over $\| \cdot \|_\infty$ implies $f_n \to f$ over $\| \cdot \|_2$ and is $(C[a,b], \|\cdot\|_2)$ Banach?

$f = g$ almost everywhere implies $f =g$ for any continuous function $f$ and $g$.

An example for an operator with closed image but zero modulus

Density and codimension

There is a complemented subspace $E$ of $l^p$ such that $T$ is an isomorphism of $E$ onto a complemented subspace $T(E)$

A continuous Function from $R$ to a Banach Space is Borel-Measurable

Showing uniqueness of holomorphic functions on Banach spaces using uniquess of scalar holomorphic functions?

A question about norm of the bounded linear operator

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