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Banach Algebras and invariant subspaces
Closed ideal theory.
Norm estimates of resolvant, Norm controlled solutions of Bézout identity
Reflexivity of operators.
Analytic function spaces
Dirichlet spaces.
Cyclicity and invariant subspaces.
Carleson measures and multipliers.
Kernel estimates and capacity.
Zero sets and Interpolation.
Composition operators compactness and approximation numbers.
Weighted Bergman spaces
Toeplitz operators, boundedness, compactness and membership to Schatten classes.
Cyclicity in large weighted Bergman spaces.