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Solvability of infinite systems of infinite linear equations. (English) Zbl 0568.15001

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)
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