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Examples of unitary spaces Real spaces
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absolutely convex arbitrary Banach algebra Banach space basis of neighbourhoods boundary conditions C*-algebra called Chapter closed coefficients commutative compact operator compact set complete constant continuous functions continuous linear Corollary countable defined denote dense derivatives differential operator dimensional Dirichlet problem domain Ehrling inequality eigenvalues element elliptic operator equation equivalent ergodic exists finite-dimensional following Theorem formula fundamental theorem Garding Hermitian operator Hilbert space holomorphic Hormander identity implies isometric isomorphism kernel Legendre form Lemma Let us observe Lie group linear functional linear map linear operators manifold maximal ideals measure neighbourhood of zero Neumann normed space nuclear obtain one-parameter open set orthonormal polynomial positive definite Proof representation satisfies scalar product Section self-adjoint extension self-adjoint operator semigroup seminorm separable Hilbert space spectral theorem spectrum subset subspace sufficient Suppose symmetric operator theory topology transformation unitary space vanishes weak solutions weakly whence