Summable endomorphisms

Let $𝑉$ be a vector space over $𝕂$ and ${𝑥 𝑖} 𝑖 \in 𝐼 \subseteq E n d 𝑉$ be a family of linear operators. We say ${𝑥 𝑖} 𝑖 \in 𝐼$ is summable iff for any $𝑣 \in 𝑉$ , $𝑥 (-) 𝑣$ has finite support, #m/def/linalg and thence¹

\sum 𝑖 \in 𝐼 𝑥 𝑖 : 𝑉 \to 𝑉 𝑣 \mapsto \sum 𝑖 \in 𝐼 𝑥 𝑖 𝑣

#state/tidy | #lang/en | #SemBr

1988. Vertex operator algebras and the Monster, §2.1, p. 49 ↩

Summable endomorphisms

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