Arlinskii Yu. Factorizations of nonnegative symmetric operators / Yu. Arlinskii, Yu. Kovalev // Methods of Functional Analysis and Topology. - 2013. - 19, № 3. - С. 211-226. - Бібліогр.: 35 назв. - англ.We prove that each closed densely defined and nonnegative symmetric operator <$E A Dot> having disjoint nonnegative self-adjoint extensions admits infinitely many factorizations of the form <$E A Dot~=~LL sub 0>, where <$E L sub 0> is a closed nonnegative symmetric operator and L its nonnegative self-adjoint extension. The same factorizations are also established for a non-denscly defined nonnegative closed symmetric operator with infinite deficiency indices while for operator with finite deficiency indices we prove impossibility of such a kind factorization. A construction of pairs <$E L sub 0~symbol <172>~L> (<$E L sub 0> is closed and densely defined, <$E L~=~L sup *~symbol У~0>) having the property dom(<$E LL sub 0>) = {0} (and, in particular, dom(<$E L sub 0 sup 2 ) = {0}) is given. Індекс рубрикатора НБУВ: В162.13
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Шифр НБУВ: Ж41243 Пошук видання у каталогах НБУВ
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