`BookProof.ChapterF7.smul_l2Symmetric` {c : ℂ} (hc : (starRingEnd ℂ) c = c) {T : 𝓢(ℝ, ℂ) →L[ℂ] 𝓢(ℝ, ℂ)} (hT : IsL2Symmetric T) : IsL2Symmetric (c • T)

Proved

BookProof.ChapterF7.smul_l2Symmetric

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF7.

BookProof.ChapterF7.smul_l2Symmetric {c : ℂ} (hc : (starRingEnd ℂ) c = c) {T : 𝓢(ℝ, ℂ) →L[ℂ] 𝓢(ℝ, ℂ)} (hT : IsL2Symmetric T) : IsL2Symmetric (c • T)

Formalization note: Lean 4 identifier BookProof.ChapterF7.smul_l2Symmetric.

Preamble

-- Generated from ChapterF7.lean — theorem BookProof.ChapterF7.smul_l2Symmetric
import Mathlib
import Definitions.Def_ChapterF7
open BookProof.ChapterF7


open SchwartzMap MeasureTheory Complex
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF7.smul_l2Symmetric {c : ℂ} (hc : (starRingEnd ℂ) c = c)
    {T : 𝓢(ℝ, ℂ) →L[ℂ] 𝓢(ℝ, ℂ)} (hT : IsL2Symmetric T) :
    IsL2Symmetric (c • T) := by sorry

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