The California Court of Appeal, Sixth District, answered this question in Sheppard v. Lightpost Museum Fund (2006) 146 Cal.App.4th 654.
In that case the court held that a superior court cannot " . . . grant a motion to strike an arbitration claim filed only in an agreed arbitral forum and not asserted by the claimant in any complaint, cross-complaint or petition filed in court."
In other words, an arbitration claim is not subject to an anti-SLAPP motion. The court came to this conclusion for two main reasons: (1) a plain reading of the statute reveals that arbitration claims are not included in the statute; and (2) the purpose of the statute is to prevent abuses of the judicial process and the judicial process is very much different than an arbitration.
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