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1 vote
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What is the socle of the $2\times 2$ matrix algebra over a Banach algebra?

$\DeclareMathOperator\soc{soc}$Let $\mathcal{A}$ be a unital semisimple Banach algebra. The socle of $\mathcal{A}$, $\soc(\mathcal{A})$ is defined as the sum of the minimal right ideals (which equals …
Qingping Zeng's user avatar
7 votes
1 answer
241 views

Does a Banach algebra version of "the sum of a closed subspace and a finite dimensional subs...

In the setting of Banach spaces, it is well know that if $M$ is a closed subspace of a Banach space $X$ and $F$ is a finite dimensional subspace of $X$, then $M+F$ is closed. Does a Banach algebra ver …
Qingping Zeng's user avatar