Functional Analysis With Step-by-step Exercises

This textbook covers the standard material of a two-semester graduate sequence in Functional Analysis, including linear topological spaces, Banach spaces, Hilbert spaces, compact operators, C*-algebras, von Neumann algebras, and unbounded operators. Particular emphasis is given to the functional calculus and the spectral theorem for both bounded and unbounded normal operators.While the material is classical, it is presented with a forward-looking perspective aimed at preparing students for further study in analysis, mathematical physics, and quantum information theory. The exposition emphasizes conceptual clarity and mathematical maturity, helping students build a strong foundation for advanced research.A distinctive feature of the textbook is the integration of exercises directly into the text, rather than collecting them at the end of each section. These exercises are carefully structured into manageable steps, guiding graduate students through key ideas and techniques while reinforcing the material as it is introduced.