List questions from banach-algebras

Published on 22 Mar 2026 - 15:44

52

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To find an element in $A$ which is invertible in $B$ but not in $A$.

Published on 20 Mar 2026 - 0:18

57

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Let $\varphi: A \to \mathbb C$ be a non-zero homomorphism. How can we extend it to an homomorphism $\psi: \overline A \to \mathbb C$?

Published on 22 Mar 2026 - 10:52

2.2k

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Prove that the set of invertible elements in a Banach algebra is open

Published on 20 Mar 2026 - 6:56

241

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Separability of differentiable functions

Published on 20 Mar 2026 - 7:23

1.4k

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An injective continuous map between two compact Hausdorff spaces.

Published on 24 Mar 2026 - 0:39

91

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Banach algebra of functions under composition

Published on 20 Mar 2026 - 10:12

60

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Double limit of a net

Published on 21 Mar 2026 - 14:39

63

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Can we characterise $X$ being separable in terms of $C(X, \mathbb R)$?

Published on 20 Mar 2026 - 2:33

289

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Unit ball of the adjoint space of a separable Banach space is second-countable in the weak* topology.

Published on 20 Mar 2026 - 5:59

53

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A is a Banach $∗$-algebra.

Published on 22 Mar 2026 - 12:14

79

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Is multiplication in a normed algebra distributive?

Published on 20 Mar 2026 - 6:45

154

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Proving that a family of exponential operators has a uniform bound, without semigroup theory.

Published on 19 Mar 2026 - 20:03

251

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First isomorphism theorem for Banach algebra

Published on 25 Mar 2026 - 4:36

460

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The maximal ideal space of $L^{\infty} ([0,1],m)$ has no isolated points.

Published on 25 Mar 2026 - 3:07

List Question

Bijection between $\Delta(A)$ and $\mathrm{Max}(A)$

To find an element in $A$ which is invertible in $B$ but not in $A$.

Let $\varphi: A \to \mathbb C$ be a non-zero homomorphism. How can we extend it to an homomorphism $\psi: \overline A \to \mathbb C$?

Prove that the set of invertible elements in a Banach algebra is open

Separability of differentiable functions

An injective continuous map between two compact Hausdorff spaces.

Banach algebra of functions under composition

Double limit of a net

Can we characterise $X$ being separable in terms of $C(X, \mathbb R)$?

Unit ball of the adjoint space of a separable Banach space is second-countable in the weak* topology.

A is a Banach $∗$-algebra.

Is multiplication in a normed algebra distributive?

Proving that a family of exponential operators has a uniform bound, without semigroup theory.

First isomorphism theorem for Banach algebra

The maximal ideal space of $L^{\infty} ([0,1],m)$ has no isolated points.

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