Dilations of Hilbert Space Operators: (general Theory) |
Contents
Introduction | 5 |
Notation and definitions | 7 |
Elementary properties of dilations | 8 |
Copyright | |
9 other sections not shown
Common terms and phrases
approximate identity Arveson Banach algebra boundedness condition C*-algebra called completes the proof complex Hilbert space Consequently define definite operator function denoted dilation theorems Dissertationes Mathematicae family of operators fe H following conditions formula functions on groups ƒ H H₁ H₂ Hence Hilbert space implies inequality involution isometry K₁ L(H₁ Lemma Let q linear map linear operator linear space matrix n-positive Naimark Neumann algebra norm null space operator valued orthogonal projection orthogonal sum positive definite function positive definite operator positive functional positive linear positive operator prove the following q is positive quasi-similarity R-dilation R₁ R₂ representation of G S₁ S₂ Section semi-group and q semi-group of operators semi-spectral measure space H spectral dilation spectral measure subspace Suppose symmetric Sz.-Nagy theory unique unitarily unitary isomorphism unitary representation vector von Neumann algebra weakly positive definite