Question

Integral of a function from a measure space into a topological vector space (Theorem 3.27 of Rudin's Functional Analysis)

score 55 · Answer 1 · 2023-05-02 21:31:36

55

Views

Integral of a function from a measure space into a topological vector space (Theorem 3.27 of Rudin's Functional Analysis)

Published on 02 May 2023 - 21:31

score 275 · Answer 2 · 2023-05-09 11:59:13

275

Views

Does the topology determine the vector space structure of a topological vector space?

Published on 09 May 2023 - 11:59

score 131 · Answer 3 · 2026-03-26 06:20:25

131

Views

Is $C^\infty([0,1]^n)$ a separable Frechet space?

Published on 26 Mar 2026 - 6:20

score 36 · Answer 4 · 2023-05-14 04:29:39

Let $C$ is a convex subset in a normed linear space, does $\mbox{Int} (C) = \mbox{Int} \left(\overline{C}\right)$ while $\mbox{Int} (C) = \emptyset$?

score 58 · Answer 5 · 2023-05-15 09:43:51

58

Views

(Dis-)continuity of the multiplication in the space $\mathcal{B}(\mathcal{H})$ of bounded linear operators on a Hilbert space

Published on 15 May 2023 - 9:43

score 50 · Answer 6 · 2023-05-16 03:33:57

50

Views

Is any topological vector space first countable?

Published on 16 May 2023 - 3:33

score 118 · Answer 7 · 2023-05-16 20:31:30

118

Views

A bounded linear operator between Frechet spaces and using balanced neighborhoods of the origin to approximate modulus of continuity

Published on 16 May 2023 - 20:31

score 98 · Answer 8 · 2023-05-29 02:08:07

98

Views

Every locally convex space has a directed family of seminorms equivalent to the family defining the space

Published on 29 May 2023 - 2:08

score 178 · Answer 9 · 2026-03-26 06:42:45

178

Views

A Hausdorff topological vector space is locally convex if and only if $0$ has a neighborhood base of balanced, convex, absorbing space

Published on 26 Mar 2026 - 6:42

score 67 · Answer 10 · 2026-03-25 19:03:00

67

Views

Hahn-Banach theorem on locally convex spaces

Published on 25 Mar 2026 - 19:03

score 62 · Answer 11 · 2026-03-25 11:08:45

62

Views

Inductive limit and denseness

Published on 25 Mar 2026 - 11:08

score 55 · Answer 12 · 2026-03-26 06:34:58

55

Views

Are the weakly bounded subsets of the double dual bounded for the natural topology?

Published on 26 Mar 2026 - 6:34

score 21 · Answer 13 · 2026-03-25 04:43:46

21

Views

Is there any way to show that the algebraic tensor product $A[[h]] \otimes A[[h]] \subsetneq (A \otimes A) [[h]]\ $?

Published on 25 Mar 2026 - 4:43

score 77 · Answer 14 · 2026-03-26 06:34:30

77

Views

The Mackey topology $\tau(X^*, X)$

Published on 26 Mar 2026 - 6:34

score 53 · Answer 15 · 2023-06-12 07:25:08

53

Views

A locally convex space has a topology given by a single norm if the topology is generated by finitely many seminorms

Published on 12 Jun 2023 - 7:25

List Question

Integral of a function from a measure space into a topological vector space (Theorem 3.27 of Rudin's Functional Analysis)

Does the topology determine the vector space structure of a topological vector space?

Is $C^\infty([0,1]^n)$ a separable Frechet space?

Let $C$ is a convex subset in a normed linear space, does $\mbox{Int} (C) = \mbox{Int} \left(\overline{C}\right)$ while $\mbox{Int} (C) = \emptyset$?

(Dis-)continuity of the multiplication in the space $\mathcal{B}(\mathcal{H})$ of bounded linear operators on a Hilbert space

Is any topological vector space first countable?

A bounded linear operator between Frechet spaces and using balanced neighborhoods of the origin to approximate modulus of continuity

Every locally convex space has a directed family of seminorms equivalent to the family defining the space

A Hausdorff topological vector space is locally convex if and only if $0$ has a neighborhood base of balanced, convex, absorbing space

Hahn-Banach theorem on locally convex spaces

Inductive limit and denseness

Are the weakly bounded subsets of the double dual bounded for the natural topology?

Is there any way to show that the algebraic tensor product $A[[h]] \otimes A[[h]] \subsetneq (A \otimes A) [[h]]\ $?

The Mackey topology $\tau(X^*, X)$

A locally convex space has a topology given by a single norm if the topology is generated by finitely many seminorms

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