Lokalno konveksni topološki vektorski prostori s hilbertskimi polnormami - Kramar, Edvard (visokošolska dela, 1977)
A locally convex topological vector spaces whose seminorms can be expressed with the semiscalar products are considered. The properties of such a space and linear operators in it are studied. The adjoint operator is defined and some theorems about the specter are proved. Various algebras of continuous operators are studied and it is shown that the algebra of the continuous operators, for which the adjoint operator exists, is a ?$LMC^*$?-algebra. In the last section the spectral decomposition for a arbitrary selfadjoint operator is proved.
Keywords: adjoint operatoru; topološki vektorski prostori; funkcionalna analiza; lokalno konveksni prostori; hilbertska polnorma; algebra operatorjev; spektri; spektralna razčlenitev