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Geometrical and topological preliminaries
Operators and their adjoint s
7 other sections not shown
A T A"1 According to Theorem assume that Q Banach space Borel set Cayley transform closed operator complex number Consequently continuous and defined continuous operators defined D(Tr denote dH(E domain D(A eigenvalue element y e exists form Q Furthermore Hermitian form Hilbert product implies that x e isometric operator JYVASKYLA K-adjoint K-normal Let us choose Let us take linear manifold majorant H majorant of Q norm normal Hilbert major obtains open mapping theorem operator of Q point of regular positive number Proof properties a)-(c Q is Hermitian Q with respect Q-unitary regular point regular type respect to H right hand normal Rolf Nevanlinna self-adjoint self-adjoint operator sesquilinear form spectral decomposition spectral family spectral measure spectrum symmetric operator Take y e Theorem 6.3 uniform Hilbert majorant unitary Hilbert majorant unitary operator unitary semi-group valid x e D(T