tsum_op — Mathlib

English

Under a suitable space condition, tsum commutes with op: tsum (op ∘ f) = op (tsum f).

Русский

При подходящем условии пространства, суммирование commuting с op: tsum (op f) = op (tsum f).

LaTeX

$$$\\operatorname{tsum}_{L} (\\lambda x, \\operatorname{op}(f x)) = \\operatorname{op}\\big( \\operatorname{tsum}_{L} f \\big)$$$

Lean4

theorem tsum_op [T2Space α] : ∑'[L] x, op (f x) = op (∑'[L] x, f x) :=
  (opHomeomorph.isClosedEmbedding.map_tsum f (g := opAddEquiv)).symm

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