List questions from gelfand-representation | MathQA

Gelfand-Naimark theorem fails for Banach algebras?

Published on 01 Jul 2021 - 10:47

What is the cardinality of $K$, where $L_\infty[0,1]=C(K)$?

Published on 24 Aug 2021 - 8:51

Gelfand-Kolmogorov-type theorem for $C_0(X)$?

Published on 28 Aug 2021 - 1:35

How to describe the Gelfand transform of the Banach algebra of complex Borel measures on the real line?

Published on 01 Oct 2021 - 12:53

Proof of Corona problem for $\mathbb{D}$

Published on 05 Nov 2021 - 16:22

How to prove this expression is a polynomial

Published on 16 Feb 2022 - 5:14

Direct sum of direct integrals

Published on 15 Mar 2022 - 23:29

Let $G=SO(3)$ and $\theta:G\to G$ defined by $\theta(g)=JgJ$ where $J=\text{diag}(-1,1,1)$. Prove that, $\theta(g)\in Kg^{-1}K$ where $K=SO(2)$

Published on 28 Mar 2022 - 21:02

An example which disproves $\|p(T)\|_{op} = \|p\|_\sup$ in arbitrary Banach spaces (Gelfand theory).

Published on 29 Jul 2022 - 22:52

Character Space of $C^1[0,1]$ and Gelfand Representation

Published on 16 Jan 2023 - 15:24