The classical Schwarz lemma for any scalar-valued holomorphic function mapping the open unit disc into itself is generalized, replacing by a holomorphic map of into a unital associative Banach algebra , and by the spectral radius of (). If and is a complex Hilbert space, the behaviour of the numerical radius of is also investigated.
Cite this article
Edoardo Vesentini, A spectral Schwarz lemma. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 4, pp. 309–323