Yılmaz F.
Turkish Journal of Mathematics and Computer Science, vol.16, no.2, pp.309-313, 2024 (Scopus, TRDizin)
Abstract
Let H" role="presentation" >H be a separable complete Pick space of continuous functions on a compact set Ω" role="presentation" >Ω with multiplier algebra M(H)" role="presentation" >M(H). The notion of the pseudo-cyclicity is recently defined by Aleman et al. In this short paper, we first extend their definition of the pseudo-cyclic multipliers to all functions f" role="presentation" >f in H" role="presentation" >H. Then we show that whenever one-function corona theorem holds for M(H)" role="presentation" >M(H) then a function f" role="presentation" >f in H" role="presentation" >H is in the pseudo-cyclic class Cn(H)" role="presentation" >Cn(H) if and only if 1/f" role="presentation" >1/f is in the corresponding Pick-Smirnov type class Nn+(H)" role="presentation" >N+n(H). Furthermore, we show that non-vanishing functions f∈H" role="presentation" >f∈H are in the class C1(H)" role="presentation" >C1(H). For functions φ,ψ" role="presentation" >φ,ψ in M(H)" role="presentation" >M(H), with at least one being in C1(H)" role="presentation" >C1(H), we also show that the invariant subspace generated by φψ" role="presentation" >φψ is equal to the intersection of invariant subspaces generated by φ" role="presentation" >φ and ψ" role="presentation" >ψ.