On Unbounded Bergman Operators |
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A₁ analytic function Area G Berger-Shaw Theroem Bergman space bounded analytic function bounded Bergman operator bounded extension bounded linear functional bounded linear operator bounded open subset bounded operator bounded real Cartesian decomposition closed densely defined closed symmetric operator dense in H dense in L² dense subset densely defined operator dim ker domain extension of spectral f in dom F. H. Szafraniec finite function on G Hence Hilbert-Schmidt operator isometric isomorphism L² G L²(D L²₂ Let fe Let G linear span M₂ minimal normal extension multiplication open problem open subset operator for G operator on H operators commuting orthonormal basis positive symmetric operator Proof S₁ self-adjoint operator self-commutator S*,S spectral type spectrum square integrable functions subset G sufficient condition T₂ Theorem 2.9 Theorem Let trace class operator unbounded subnormal operators whole plane