Abstract
Some principles of the operator theory in a linear space with two norms are established in this paper. The well-known Hilbert-Schmidt theorem on the eigenfunction expansion of sourcewise represented functions, Mercer's theorem and other results can be consider as special cases of the statements presented. The general approach proposed is used to construct the theory of symmetrizable operators and to investigate the asymptotic behaviour of eigenvalues of compact operators.
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Additional information
This paper was translated by M. Gorbuchuk and V. Gorbachuk
This paper was translated by M. Gorbuchuk and V. Gorbachuk.