We consider the generalised Hahn sequence space \(h_{d}\), where d is an unbounded monotone increasing sequence of positive real numbers, and characterise several classes of bounded linear operators or matrix transformations from \(h_{d}\) into the spaces of all bounded, convergent and null sequences, and into the space of all abolutely convergent series and \(h_{d}\), and also from spaces of all absolutely convergent series, all null, convergent and bounded sequences into \(h_{d}\). Furthermore, we establish identities or estimates for the norms of the corresponding bounded linear operators. We also derive identities for the Hausdorff measure of noncompactness for the operators in the above classes with the exception of the final space being the space of all bounded sequences and charcaterise the classes of all corresponding compact operators. Finally, we apply our results to present a Fredholm operator from \(h_{d}\) into itself given by a tridiagonal matrix.

我们考虑广义哈恩序列空间\(h_{d}\)，其中d是一个无界单调递增的正实数序列，并刻画了几类有界线性算子或矩阵变换从\(h_{d}\)到所有有界、收敛和空序列的空间，并进入所有绝对收敛级数和\(h_{d}\) 的空间，也从所有绝对收敛级数的空间，所有空、收敛和有界序列进入\(高清}\）. 此外，我们为相应的有界线性算子的范数建立恒等式或估计。除了最终空间是所有有界序列的空间之外，我们还导出了上述类中算子的 Hausdorff 非紧凑性度量的恒等式，并表征了所有相应紧凑算子的类。最后，我们应用我们的结果来呈现一个 Fredholm 算子从\(h_{d}\)到由三对角矩阵给出的自身。