Synopses & Reviews
This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry.
Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Extensive appendixes offer supplemental information on the graph of a linear operator and the Riemann-Stieltjes and Lebesgue integration.
Synopsis
Starting with a definition of Hilbert space and its geometry, this text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Familiarity with analysis and analytic geometry is the only prerequisite. Extensive appendixes complement the text. 1969 edition.
Synopsis
This introduction to Hilbert space, bounded self-adjoint operators, the spectrum of an operator, and operators' spectral decomposition is accessible to readers familiar with analysis and analytic geometry. 1969 edition.
Table of Contents
I. The concept of Hilbert spaceII. Specific geometry of Hilbert spaceIII. Bounded linear operatorsIV. General theory of linear operatorsV. Spectral analysis of compact linear operatorsVI. Spectral analysis of bounded linear operatorsVII. Spectral analysis of unbounded selfadjoint operatorsAppendix A. The graph of a linear operatorAppendix B. Riemann-Stieltjes and Lebesgue integrationBibliographyIndex of symbolsSubject index