Ferrera Cuesta, Juan2023-06-202023-06-2020020039-322310.4064/sm151-1-1https://hdl.handle.net/20.500.14352/57243We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Frechet differentiable: We also characterize the Gateaux differentiability of the norm. Finally we study those properties for some classical Banach spaces.engjournal articlehttp://journals.impan.gov.pl/open access517.986.6517.518.45Banach spacesPolynomialsNorm differentiabilityShmul'yans's testStrongly attains its normFréchet differentiabilityGâteaux differentiabilityAnálisis matemático1202 Análisis y Análisis Funcional