We present new results regarding S2-paracompactness, that we estab-lished in [1], and its relation with other properties such as S-normality, epinormality L-paracompactness.

We determine all tight Lagrangian surfaces in S2×S2. In particular, globally tight Lagrangian surfaces in S2 × S2 are nothing but real forms.

A class of algebras is introduced that includes the unital Banach algebras over the complex numbers. Commutator results are proved for such algebras and used to establish spectral properties of certain elements of Banach algebras. 1. Introduction. In this note, we introduce a condition on an algebra motivated by the situation in which Schur's lemma [S1] is applicable. We say that algebras satis...