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Some Reminders of Functional Analysis
Some Classes of Operators
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A G D algebra and let algebra with involution analytic function analytic multifunction argument Banach space bounded linear operator C*-algebra C*-algebra and let capacity zero Chapter closed subalgebra commutative Banach algebra compact operators compact set compact subset conclude Consequently constant contains continuous irreducible representation converges Corollary countable DaK(X defined denote disjoint disk domain easy to verify eigenvalue EXERCISE finite finite-dimensional following properties Gelfand Hence Hilbert space Holomorphic Functional Calculus hypothesis identity invertible irreducible representation isolated point isomorphic Lemma Let f Let H linear functional linear subspace linearly independent maximal left ideal Mn(C Moreover morphism neighbourhood nilpotent norm obvious open set open subset plurisubharmonic polynomial prove pseudoconvex pseudoconvex open subset quasi-nilpotent elements result self-adjoint semi-simple semi-simple Banach algebra set of holomorphy Sp(x space and let spectral theory subharmonic functions Suppose topology unit ball upper semicontinuous