caa a22 4500 46797960X CHVBK 20180323112515.0 cr unu---uuuuu 170328e19900501xx s 000 0 eng 10.1007/BF02844765 doi (NATIONALLICENCE)springer-10.1007/BF02844765 Abian Alexander Department of Mathematics, Iowa State University, 50011, Ames, Iowa, USA aut An inner product and orthonormalization in l p -spaces and solution of infinite systems of infinite linear equations [Elektronische Daten] [Alexander Abian] Let the rows of an infinite square matrixM be elements ofl p -space (p>1) andX be an infinite column vector of unknowns andC an infinite column vector of real numbers. To our knowledge the solvability ofMX=C has nowhere been satisfactorily studied in the literature. This is also true of Riesz'classical work [2]. A reason for this is that not until recently [1] an appropriate inner product and the corresponding orthonormalization forp≠2 has been introduced. In this paper, based on [1], it is shown thatMX=C has a solution which is an element ofl q if and only if upon our process of orthonormalization of the rows ofM the system yields an equivalent systemAX=K where the rows ofA form an orthonormal sequence (in our sense) of elements ofl p andK becomes an element ofl q withp −1+q −1=1. A solution is then given byX=(A (q) (AA (q) )−1)K whereA (q) is ourq-transpose ofA. This solution is the solution of the minimall q -norm. Otherwise, the obvious dual concept of the best approximating solution inl q -norm is introduced and obtained. Springer, 1990 Rendiconti del Circolo Matematico di Palermo Springer-Verlag 39/2(1990-05-01), 307-314 0009-725X 39:2<307 1990 39 12215 https://doi.org/10.1007/BF02844765 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02844765 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Abian Alexander Department of Mathematics, Iowa State University, 50011, Ames, Iowa, USA aut NATIONALLICENCE 773 0- Rendiconti del Circolo Matematico di Palermo Springer-Verlag 39/2(1990-05-01), 307-314 0009-725X 39:2<307 1990 39 12215 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer