Hilbert Spaces and Operator Theory
Emphasizing a clear exposition for readers familiar with elementary measure theory and the fundamentals of set theory and general topology, presents the basic notions and methods of the theory of Hilbert spaces, a part of functional analysis being increasingly applied in mathematics and theoretical
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Special Classes of Linear Operators
3 other sections not shown
adjoint operator arbitrary assume Banach algebra belongs bilinear form Borel measure called closable closed operator closed subspace closure commute complete condition Consequently consider continuous function convergent countable decomposition definition denote densely defined Dirichlet algebra element equality Example finite follows formula Hence Hilbert space hyponormal implies inequality involution isometry Lebesgue measure Lemma linear operator linear space linearly dense measure F metric space morphism nonnegative normal operator normed space obtain operator norm operator of multiplication orthogonal sum orthonormal polynomials pre-Hilbert space projection Proof properties proved real-valued reduces representation resp satisfies scalar product Section self-adjoint operator semi-group semi-norm semi-spectral measure sequence xn space H spectral integrals spectral measure subalgebra subset Suppose symmetric operator Theorem topology unitarily equivalent unitary isomorphism unitary operator vector write x e 2(A x e H y e H zero