Multiplicative sequences for universal sequences of mappings (Q2770651)

Let \(X\) be a topological space and \(Y\) be a real or complex topological vector space. In this paper the author proves that if \(X\) and \(Y\) satisfy certain assumptions and \(T_n:X\longrightarrow Y\) is a densely universal sequence of continuous mappings then, for ''most'' scalar sequences \((c_n)\), the sequence of mappings \((c_nT_n)\) is also densely universal (Section 2). In Section 3 he proves that if \(T\) is a hypercyclic operator on a Baire metrizable complex locally convex space then there exists a residual subset \(B\) in the unit circle such that \(\lambda T\) is also hypercyclic for all \(\lambda \in B\).