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A Lemma Concerning Convex Functionals
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adjoint operator arbitrary assume belongs bilinear bounded linear operator bounded operator called closed linear closed linear operator closure completely continuous operator complex number conjugation operator consider Corollary corresponding countable definition denote dense in H domain each/e Dr eigenmanifold eigenvalue eigenvector element g equation everywhere in H follows formula G reduces h e H Hence Hilbert space implies inequality integral invariant subspace inverse operator isometric operator lemma Let G linear envelope linear functional linear manifold linear operators defined linearly independent matrix representation norm operators defined everywhere orthogonal orthonormal basis orthonormal sequence orthonormal system Parseval relation periodic functions polynomials projection operator Proof proposition real axis reduces the operator regular point right member scalar product self-adjoint operator sequence of vectors solvable space H subspace G symmetric operator theorem is proved theory Translator's Note unitary operator vector g vector h e whole space zero