Inspired by a recent article on Fréchet spaces of ordinary Dirichlet series \(\sum a_n n^{-s}\) due to J. Bonet, we study topological and geometrical properties of certain scales of Fréchet spaces of general Dirichlet spaces \(\sum a_n e^{-\lambda _n s}\) focus on the Fréchet space of \(\lambda \)-Dirichlet series \(\sum a_n e^{-\lambda _n s}\) which have limit functions bounded on all half planes strictly smaller than the right half plane \([{{\,\mathrm{Re}\,}}>0]\). We develop an abstract setting of pre-Fréchet spaces of \(\lambda \)-Dirichlet series generated by certain admissible normed spaces of \(\lambda \)-Dirichlet series and the abscissas of convergence they generate, which allows also to define Fréchet spaces of \(\lambda \)-Dirichlet series for which \(a_n e^{-\lambda _n/k}\) for each k equals the Fourier coefficients of a function on an appropriate \(\lambda \)-Dirichlet group.

受J. Bonet最近一篇关于普通狄利克雷级数的 Fréchet 空间\(\sum a_n n^{-s}\) 的启发，我们研究了一般狄利克雷空间的某些尺度的 Fréchet 空间的拓扑和几何性质\(\ sum a_n e^{-\lambda _n s}\)关注\(\lambda \) -Dirichlet 系列\(\sum a_n e^{-\lambda _n s}\)的 Fréchet 空间，它们的极限函数有界所有半平面严格小于右半平面\([{{\,\mathrm{Re}\,}}>0]\)。我们开发的预Fréchet可空间的抽象设置\（\拉姆达\） -Dirichlet由某些受理赋范空间产生的系列\（\拉姆达\）-Dirichlet 级数和它们生成的收敛横坐标，这也允许定义\(\lambda \) 的Fréchet 空间-Dirichlet 级数其中\(a_n e^{-\lambda _n/k}\)对于每个k等于函数在适当的\(\lambda \) -Dirichlet 群上的傅立叶系数。