Can a judge order an appeal against a sentence that was improperly entered into the context of a criminal case?

Cal.App.4th 543, 547-548.) However, our high court has "created a narrow exception to the [forfeiture] rule for ' "unauthorized sentences" or sentences entered in "excess of jurisdiction." ' [Citation.] Because these sentences 'could not lawfully be imposed under any circumstance in the particular case' [citation] they are reviewable 'regardless of whether an objection or argument was raised in the trial and/or reviewing court.' [Citation.]" (People v. Smith (2001) 24 Cal.4th 849, 852.) Our high court deemed "appellate intervention appropriate in these cases because the errors presented 'pure questions of law' [citation] and were ' "clear and correctable" independent of any factual issues presented by the record at sentencing.' [Citation.] In other words, obvious legal errors at sentencing that are correctable without referring to factual findings in the record or remanding for further findings are not [forfeited]." (Ibid.)