Abian, Alexander; Eslami, Esfandiar Solvability of infinite systems of infinite linear equations. (English) Zbl 0568.15001 Bol. Soc. Mat. Mex., II. Ser. 27, 57-64 (1982). Consider the system \(S:\sum^{\infty}_{i=1}a_{ki}x_ i=c_ k,\) \(k=1,2,...\), \(a_{ki},c_ k\in R,\) \(i,k=1,2,... \). Under the conditions: p,q\(\in R\) with \(1/p+1/q=1\) and \(p>1\); \(\sum^{\infty}_{i=1}| a_{ki}|^ q<\infty\) for every \(k=1,2,...\); \(M>0\) (preassigned) the following main result is formulated. S has the solution \(x_ i=r_ i\), \(i=1,2,...\), with \(\sum^{\infty}_{i=1}| r_ i|^ p\leq M^ p\), if and only if every finite subsystem of S has a solution with the same property. Reviewer: M.Voicu MSC: 15A06 Linear equations (linear algebraic aspects) 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:infinite systems of infinite linear equations; solution in sequence space \(L_ p\) PDFBibTeX XMLCite \textit{A. Abian} and \textit{E. Eslami}, Bol. Soc. Mat. Mex., II. Ser. 27, 57--64 (1982; Zbl 0568.15001)