The question whether every operator on H has an hyperinvariant subspace is one of the most difficult problems in operator theory. The purpose of this paper is to make a beginning on the hyperinvariant subspace problems for another class of operators closely related to the normal operators namely, the class of k -quasi-class A operators. A necessary and sufficient condition for the hypercyclicit...

We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω . The orbit is taken with respect to any fixed nonscalar differential operator generated by an entire function of subexponential type, thereby ext...

Let (X, T ) be a topological dynamical system (TDS), and h(T, K) the topological entropy of a subset K of X . (X, T ) is lowerable if for each 0 ≤ h ≤ h(T, X) there is a non-empty compact subset with entropy h; is hereditarily lowerable if each non-empty compact subset is lowerable; is hereditarily uniformly lowerable if for each non-empty compact subset K and each 0 ≤ h ≤ h(T, K) there is a no...

A space X is submaximal if any dense subset of open. In this paper, we prove that every topological gyrogroup non-measurable cardinality strongly ?-discrete. Moreover, hereditarily paracompact.