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Yu. Kovalev

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Articles: 1

Factorizations of nonnegative symmetric operators

Yury Arlinskiĭ, Yury Kovalev

↓ Abstract   |   Article (.pdf)

MFAT 19 (2013), no. 3, 211-226

211-226

We prove that each closed denselydefined and nonnegative symmetric operator ˙A having disjointnonnegative self-adjoint extensions admits infinitely manyfactorizations of the form ˙A=LL0, where L0 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 L0L (L0 isclosed and densely defined, L=L0) having the propertydom(LL0)={0} (and, in particular, dom(L20)={0}) is given.


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