A refined polar decomposition for J-unitary operators - Zagorodnyuk, Sergey M. (Sarajevo Journal of Mathematics, 2015)
In this paper, we will characterize the components of the polar decomposition for an arbitrary J-unitary operator in a Hilbert space (where J is a conjugation). This characterization has a quite different structure from that of symmetric and complex skew-symmetric operators. It is also shown that for a J-imaginary closed symmetric operator in a Hilbert space there exists a J-imaginary self-adjoint extension in a possibly larger Hilbert space (a linear operator A in a Hilbert space H is said to be J-imaginary if fD(A) implies JfD(A) and AJf = -JAf, where J is a conjugation on H.) All Hilbert spaces in this paper are assumed to be separable.