List questions from banach-algebras

Published on 25 Mar 2026 - 11:12

111

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

Published on 01 Nov 2018 - 15:30

38

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Can C*-envelope introduce the unity?

Published on 09 Nov 2018 - 21:32

73

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Approximate identity in $\ell _p$

Published on 17 Nov 2018 - 10:40

41

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$C^*$ algebra, existence of particular state

Published on 17 Nov 2018 - 13:22

101

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In Banach algebra $A$ if $ab=ba$ prove that $e^{a+b}=e^ae^b$

Published on 19 Nov 2018 - 17:51

53

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If $A$ is invertible and $r^{\text{Gelf}}(BA^{-1}) < 1$, then $(A - B)$ is invertible.

Published on 20 Nov 2018 - 17:41

81

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$\mathcal{E}(C(K, \mathbb{C})) = \{\omega_a : a \in K\}$

Published on 23 Nov 2018 - 15:58

63

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$A$ self-adjoint, $f \in C(\sigma(A), \mathbb{C})$, then $\sigma(f(A)) = f(\sigma(A))$

Published on 25 Nov 2018 - 11:50

49

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Lemma 5.1.5 from Garth Dales, Introduction to Banach algebra

Published on 01 Dec 2018 - 12:55

207

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Prove that in a Banach algebra, the connected component of the set of invertible elements containing the identity is a normal subgroup

Published on 06 Dec 2018 - 23:08

379

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Rudin Functional Analysis, Chapter $10$, exercise $12$

Published on 12 Dec 2018 - 20:30

127

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Spectrum of Banach algebra with coordinate multiplication

Published on 13 Dec 2018 - 22:03

166

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Gelfand transformation of $l^p$

Published on 23 Mar 2026 - 1:54

33

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Lower bound for the speed convergence of the spectrum

Published on 25 Mar 2026 - 7:48

List Question

Existence of a holomorphic function on the unit disk

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

Can C*-envelope introduce the unity?

Approximate identity in $\ell _p$

$C^*$ algebra, existence of particular state

In Banach algebra $A$ if $ab=ba$ prove that $e^{a+b}=e^ae^b$

If $A$ is invertible and $r^{\text{Gelf}}(BA^{-1}) < 1$, then $(A - B)$ is invertible.

$\mathcal{E}(C(K, \mathbb{C})) = \{\omega_a : a \in K\}$

$A$ self-adjoint, $f \in C(\sigma(A), \mathbb{C})$, then $\sigma(f(A)) = f(\sigma(A))$

Lemma 5.1.5 from Garth Dales, Introduction to Banach algebra

Prove that in a Banach algebra, the connected component of the set of invertible elements containing the identity is a normal subgroup

Rudin Functional Analysis, Chapter $10$, exercise $12$

Spectrum of Banach algebra with coordinate multiplication

Gelfand transformation of $l^p$

Lower bound for the speed convergence of the spectrum

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