On the space \(G(\lambda)\) of entire functions (Q801248)

\textit{D. Somasundaram} in Ind. J. Pure Appl. Math. 5, 921-932 (1974; Zbl 0247.46024), has studied a Hilbert space \(G(\lambda)\) of entire Talyor series defined by: \(G(\lambda)=\{f(z)=\sum^{\infty}_{n=0}a_ nz^ n;\sum^{\infty}_{n=0}\lambda_ n| a_ n|^ 2<\infty \},\) where \(\{\lambda_ n\}\) is a sequence of positive reals such that \(\{\lambda^{1/n}\}\uparrow \infty\) as \(m\to \infty\). A pointwise multiplier from \(G(\lambda)\) to \(G(\mu)\) is a function h such that \(hf\in G(\mu)\), (\(\forall)\) \(f\in G(\lambda)\). The authors studied the multipliers bewteeen \(G(\lambda)\) and various other Frechet spaces. They have improved two results about these multipliers contained in Somasundaram's work. In the second part of the work, the authors have defined a weighted Hadamard multiplication on \(G(\lambda)\) and they proved that \(G(\lambda)\) has a Banach algebra structure with this multiplication and they have characterized the topological zero divisors and the quasi-invertible elements.