Providing an introduction to the main areas of modern analysis, this text starts with general topology and moves on to normed and semi-normed linear spaces. From there, it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various possible forms of the spectral theorem: from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The work concludes with two supplementary chapters: an account of unbounded operators and their spectral ...
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Providing an introduction to the main areas of modern analysis, this text starts with general topology and moves on to normed and semi-normed linear spaces. From there, it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various possible forms of the spectral theorem: from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The work concludes with two supplementary chapters: an account of unbounded operators and their spectral theory, and a complete course in measure and integration theory (from an advanced perspective).
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