Linear Operators on Krein SpacesDivision of Applied Mathematics, Research Institute of Applied Electricity, Hokkaido University, 1979 - Hilbert space - 118 pages |
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According to Corollary According to Theorem analytic continuation angular operator ator Ax,x B₁ B₂ bijection bounded linear operator canonical decomposition compact contained defined correspondingly double commutant eigenvalues follows from Corollary follows from Theorem fractional-linear map gative gonal H+H_ H₁ hence Hilbert space idempotent implies injective inner product inner product x,y invariant J-biexpansive operator J-expansive J-inner J-negative J-orthogonal J-partial isometry J-polar decomposition J-positive operator J-projection J-unitary operator ker(A ker(U Krein and Smuljan Krein space Let us define maximal negative subspace maximal positive subspace maximal strictly positive maximal uniformly positive mutually equivalent negative according non-negative orthogonal orthoprojection positive linear manifold positive sub positive vector proof of Theorem proved analogously ran F ran(S Riesz theorem selfadjoint operator spectral function spectrum suffices to prove Suppose Theorem 1.3 theorem e.g. tive uniformly positive subspace unitary weak operator topology