An invitation to operator theory

TL;DR: For warped products with harmonic curvature, nonconstant warping functions φ, and compact two-dimensional bases (M,h), this paper established a dichotomy: either the Gaussian curvature K of the metric g = φh is constant and negative, or φ equals a specific elementary function of K, also depending on the dimension p and Einstein constant ε of the fibre.

TL;DR: In this article, it was shown that there exists a non-separable Banach space constructed by A.Arvanitakis, S.Argyros and A.Tolias such that the J-set of every operator on this space has empty interior for each non-zero vector.

TL;DR: The strongly order continuous and strongly σ-order continuous operators were introduced in this paper. But they do not consider continuous linear functionals on Riesz spaces, and they cannot be seen as continuous operators on continuous linear functions.