On the connection between the properties of completeness and unconditional convergence for orthogonal systems

A. A. Talalyan


Abstract: It is proved that there exists an orthonormal system that is not a system of unconditional convergence and, moreover, is not complete in the $L_2$-metric on any set of positive measure.
Bibliography: 8 titles.

UDC: 517.52

MSC: Primary 42C10, 42C20, 42C30; Secondary 46B15, 46E30

Received: 05.08.1981

 English version: Mathematics of the USSR-Sbornik, 1983, 45:4, 507–513

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