Let $2\leq p<\infty $ and X be a complex infinite-dimensional Banach space. It is proved that if X is p-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space $\mathscr {H}^{\text {weak}}_p(X)$ to the Hardy space $\mathscr {H}^+_p(X)$ of vector-valued Dirichlet series. To obtain this, a Littlewood–Paley inequality for Dirichlet series is established.

We give sufficient conditions for the essential spectrum of the Hermitian square of a class of Hankel operators on the Bergman space of the polydisc to contain intervals. We also compute the spectrum in case the symbol is a monomial.

This article describes Hilbert spaces contractively contained in certain reproducing kernel Hilbert spaces of analytic functions on the open unit disc which are nearly invariant under division by an inner function. We extend Hitt’s theorem on nearly invariant subspaces of the backward shift operator on $H^2(\mathbb {D})$ as well as its many generalizations to the setting of de Branges spaces.

In this paper, we show existence of bountiful examples of Gorenstein local rings A and B such that there is a triangle equivalence between the stable categories CM(A), CM(B).

We characterize the compact elements and the hypocompact radical of a crossed product $C_0(X)\times _\phi \mathbb Z$, where X is a locally compact metrizable space and $\phi :X\rightarrow X$ is a homeomorphism, in terms of the corresponding dynamical system $(X,\phi )$.