Factorizations of nonnegative symmetric operators - Arlinskii, Yu. M.; Kovalev, Yu. (Methods of Functional Analysis and Topology, 2013)
We prove that each closed denselydefined and nonnegative symmetric operator A having disjointnonnegative self-adjoint extensions admits infinitely manyfactorizations of the form A=LL_0, where L_0 is aclosed nonnegative symmetric operator and L its nonnegativeself-adjoint extension. The same factorizations are also establishedfor a non-densely defined nonnegative closed symmetric operator withinfinite deficiency indices while for operator with finitedeficiency indices we prove impossibility of such a kindfactorization. A construction of pairs L_0L (L_0 isclosed and densely defined, L=L^*0) having the propertydom (LL_0)={0} (and, in particular, dom (L^2_0)={0}) is given.