The finitistic dimension of an Artin algebra with radical square zero

We investigate the inequality Findim ? ? o p ?<!-- ? <mml:mi>dell \operatorname {Findim} \Lambda ^{op} \leq \operatorname {dell} \Lambda between finitistic dimension and delooping level of an Artin algebra alttext="normal encoding="application/x-tex">\Lambda , whether equality holds in general. prove that equals = = always for algebras with radical square zero.