Given a person commits an obvious infraction1 of a law B and this law has a sentence established by a legal statute that does not consider jury consultations possible, is there some legal framework to be sanctioned without trial?
1Say confessing to the infraction or getting caught in the act.
In the US, if a person enters a guilty plea, a judge may proceed to convict and sentence the accused without any form of trial.
In the case of minor offenses with possible penalties of less than six months in jail, there is no US constitutional right to a jury trial. and the accused may be convicted and sentenced after a bench trial with no jury.
In the case of infractions that are not criminal, such as many traffic offenses, a judge or magistrate may make a judgment and impose a penalty after a brief and often informal hearing.
In some non-US jurisdictions, there is no right to a jury trial even in serious cases. In most such jurisdictions some form of due process and some hearing or trial is required for conviction.
However, in various authoritarian regimes, people may be "convicted" of "crimes" without anything like a trial before an independent tribunal.
In short, this depends on the nature of the case, and the laws of the jurisdiction involved.
In the US, this can happen for contempt of court if it happens in open court. If the judge thinks the contempt needs to be dealt with immediately, they can convict and sentence on the spot. The person in contempt is not entitled to notice or a formal chance to defend themselves (although they basically always get a chance to say something).
There are some limits. First, any sentence over six months triggers a right to a full jury trial. Second, if the judge doesn't immediately issue the contempt ruling, they need to give the person notice and a chance to defend themselves, although not necessarily a full trial. Third, the judge needs to have personally seen all the relevant facts. Fourth, an appeals court can consider whether the contempt really needed to be handled on the spot. In state courts, state law might impose more requirements (like requiring more of a hearing for all summary contempts).
The other answers have addressed criminal and quasi-criminal cases.
In civil lawsuits seeking relief from non-criminal wrongs, judgment is routinely entered by default (for failure to file an answer or response or objection by the court deadline for doing so), or prior to trial based upon a motion for summary judgment asserting that there are no disputed issues of fact that prevent judgment from entering. Also, the vast majority of civil cases where there is not a default judgment settle rather than being resolved involuntarily on the merits.
There are a variety of non-criminal sanctions that can be applied without a formal trial. Entry on the no-fly list is done as a purely administrative matter. Restraining orders can be placed ex parte, and even when there's a hearing, the hearing doesn't have the same due process rights as a criminal trial. Involuntary commitments can also be ordered without the full due process rights of a criminal trial.
