List questions from banach-algebras

Published on 22 Apr 2022 - 17:59

34

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Show $f\in C(\mathbb{T})$ where $f(z)\neq0$ for all $z$, with summabel Fourier coefficients is invertible.

Published on 24 Apr 2022 - 18:24

40

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Is $r \in \text{Rad}(A)$?

Published on 28 Apr 2022 - 7:55

253

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The space of functions vanish at infinity

Published on 01 May 2022 - 14:21

170

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Solutions of a Linear Differential Equation in a Banach Algebra

Published on 04 May 2022 - 17:08

147

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an inequality for completely positive maps

Published on 05 May 2022 - 7:48

147

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Banach space with continuous multiplication is a Banach algebra

Published on 11 May 2022 - 15:06

91

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Understanding the proof of Fuglede's theorem

Published on 11 May 2022 - 19:35

218

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Banach algebra $L^1(\mathbb{R})$ and its Fourier transform.

Published on 16 May 2022 - 9:12

109

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Why is it difficult to define a direct integral of Banach spaces or Banach algebras?

Published on 01 Apr 2026 - 1:30

112

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If an element in a Banach algebra is anihilated by an analytic function then it must be algebraic.

Published on 24 Feb 2026 - 13:47

155

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Continuity of product in Banach Algebras

Published on 18 May 2022 - 20:39

128

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One parameter group of elements of a banach algebra

Published on 02 Jun 2022 - 15:22

81

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The invertibility of matrix in Banach algebra

Published on 04 Jun 2022 - 10:29

99

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$\lVert a \rVert = 1 = \lVert a^{-1} \rVert \Rightarrow a^* = a^{-1}$

Published on 04 Jun 2022 - 18:36

List Question

Example of an algebra that is a Banach space but not a Banach algebra

Show $f\in C(\mathbb{T})$ where $f(z)\neq0$ for all $z$, with summabel Fourier coefficients is invertible.

Is $r \in \text{Rad}(A)$?

The space of functions vanish at infinity

Solutions of a Linear Differential Equation in a Banach Algebra

an inequality for completely positive maps

Banach space with continuous multiplication is a Banach algebra

Understanding the proof of Fuglede's theorem

Banach algebra $L^1(\mathbb{R})$ and its Fourier transform.

Why is it difficult to define a direct integral of Banach spaces or Banach algebras?

If an element in a Banach algebra is anihilated by an analytic function then it must be algebraic.

Continuity of product in Banach Algebras

One parameter group of elements of a banach algebra

The invertibility of matrix in Banach algebra

$\lVert a \rVert = 1 = \lVert a^{-1} \rVert \Rightarrow a^* = a^{-1}$

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