Elements of Hilbert Spaces and Operator Theory

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Focusing on the geometry of Hilbert spaces and operator theory, this book serves as a comprehensive resource for graduate and senior undergraduate mathematics students. It covers essential topics such as inner product spaces, linear operators, and spectral theory, while exploring the structure imposed on vector spaces. Applications across various mathematical fields are examined, alongside the introduction of orthogonal polynomials in Fourier series. Key discussions include the spectrum of different operator classes and spectral theorems, with numerous examples illustrating these concepts.