Question

$\lambda$-sum of $L^1$ is a Banach space

score 35 · Answer 1 · 2026-03-25 07:42:17

35

Views

$\lambda$-sum of $L^1$ is a Banach space

Published on 25 Mar 2026 - 7:42

score 83 · Answer 2 · 2026-03-28 11:53:37

83

Views

Riemann integral in a Banach space

Published on 28 Mar 2026 - 11:53

score 29 · Answer 3 · 2023-06-15 17:28:20

29

Views

Equivalent definition of uniform convexity by an increasing function $\delta$

Published on 15 Jun 2023 - 17:28

score 80 · Answer 4 · 2026-03-28 04:35:57

80

Views

Brezis' exercise 6.2.3: is it true that $\|Tu_{n_k} - v_1\|_\infty \xrightarrow{k \to \infty} 0$?

Published on 28 Mar 2026 - 4:35

score 93 · Answer 5 · 2023-06-16 14:26:05

93

Views

Brezis' exercise 6.2.3: $T(B)$ is not closed

Published on 16 Jun 2023 - 14:26

score 95 · Answer 6 · 2026-03-28 04:35:05

95

Views

Brezis' exercise 6.3: there is a sequence $(u_n)$ in $E$ such that $|u_n|_E=1$ and $|Tu_n|_F \to 0$

Published on 28 Mar 2026 - 4:35

score 51 · Answer 7 · 2026-03-28 06:09:49

51

Views

Brezis' exercise 6.4: is the continuous injection from $\ell^p$ to $c_0$ compact?

Published on 28 Mar 2026 - 6:09

score 41 · Answer 8 · 2023-06-17 16:54:08

41

Views

Does $\iota: V\longrightarrow H$ densely imply $\iota^\top:H'\longrightarrow V'$ dense?

Published on 17 Jun 2023 - 16:54

score 84 · Answer 9 · 2026-03-28 04:35:45

84

Views

Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

Published on 28 Mar 2026 - 4:35

score 65 · Answer 10 · 2026-03-26 21:26:00

65

Views

Is there a sequence $(x_n) \subset E$ such that $|x_n|=1$ for all $n$ and that $x_n \to 0$ in $\sigma(E, E^*)$?

Published on 26 Mar 2026 - 21:26

score 94 · Answer 11 · 2023-06-18 15:07:02

94

Views

Finite dimensional cokernel of a map coming from a product Fedholm map

Published on 18 Jun 2023 - 15:07

score 45 · Answer 12 · 2026-03-25 17:42:20

45

Views

Positivity of semigroup $(P_t)_{t\geq0}$ implies its contractivity, $\| P_tf\| \leq \|f\|$

Published on 25 Mar 2026 - 17:42

score 36 · Answer 13 · 2026-03-26 08:23:03

36

Views

Every weak neighborhood of $0$ contains a finite co-dimensional subspace

Published on 26 Mar 2026 - 8:23

score 63 · Answer 14 · 2026-03-26 13:01:02

63

Views

Brezis' exercise 6.7.1: a characterization of finite-rank operators

Published on 26 Mar 2026 - 13:01

score 93 · Answer 15 · 2026-03-28 08:09:38

93

Views

Brezis' exercise 6.8: a compact operator with closed range is a finite-rank operator

Published on 28 Mar 2026 - 8:09

List Question

$\lambda$-sum of $L^1$ is a Banach space

Riemann integral in a Banach space

Equivalent definition of uniform convexity by an increasing function $\delta$

Brezis' exercise 6.2.3: is it true that $\|Tu_{n_k} - v_1\|_\infty \xrightarrow{k \to \infty} 0$?

Brezis' exercise 6.2.3: $T(B)$ is not closed

Brezis' exercise 6.3: there is a sequence $(u_n)$ in $E$ such that $|u_n|_E=1$ and $|Tu_n|_F \to 0$

Brezis' exercise 6.4: is the continuous injection from $\ell^p$ to $c_0$ compact?

Does $\iota: V\longrightarrow H$ densely imply $\iota^\top:H'\longrightarrow V'$ dense?

Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

Is there a sequence $(x_n) \subset E$ such that $|x_n|=1$ for all $n$ and that $x_n \to 0$ in $\sigma(E, E^*)$?

Finite dimensional cokernel of a map coming from a product Fedholm map

Positivity of semigroup $(P_t)_{t\geq0}$ implies its contractivity, $\| P_tf\| \leq \|f\|$

Every weak neighborhood of $0$ contains a finite co-dimensional subspace

Brezis' exercise 6.7.1: a characterization of finite-rank operators

Brezis' exercise 6.8: a compact operator with closed range is a finite-rank operator

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