Harmonic Analysis of Operators on Hilbert Space

A₁ accretive operator bounded operator boundedly invertible c.n.u. contraction Cayley transform characteristic function cogenerator coincides commuting completely non-unitary concludes the proof condition consequently contraction of class contractive analytic function converges corresponding decomposition deduce defect indices defined denote dissipative operators eigenvalue equal exists a contractive finite functional calculus H₁ H²(E Hilbert space holomorphic hyperinvariant implies inner divisor inner function invariant subspace isometric isometric dilation L²(E Lemma matrix maximal accretive minimal function minimal unitary dilation Moreover multiplication by eit non-trivial non-zero obtain obvious orthogonal projection outer function particular proved purely contractive quasi-affine quasi-similar regular divisor regular factorization relation scalar multiple scalar valued self-adjoint operator semi-group of contractions space H spectral spectrum subset T₁ U₁ unicellular unilateral shift unit circle unit disc unitarily equivalent unitary constant unitary operator V₁ vector virtue of Proposition weak contraction