Functional Analysis Revisited

Adam Bobrowski is a professor in the Department of Mathematics at Lublin University of Technology, Poland. He was awarded the Hugo Steinhaus Prize for his achievements in analyzing mathematical models of biological reality and has authored more than 70 scientific papers and six books. His works include 'Functional Analysis for Probability and Stochastic Processes' (2005), 'Convergence of One-Parameter Operator Semigroups' (2016), and 'Generators of Markov Chains' (2020).

'This is a remarkable book whose concept is not to present a comprehensive overview of a field but, keeping the geographical metaphor, it follows one of the main rivers there, exploring its tributaries and distributaries and going even beyond the boundaries of the original territory. In this case, the author follows the river of completeness of normed spaces and presents its sources in more fundamental areas of mathematics and its impact on an array of theoretical and applied fields. The book is written in an effortless, casual, yet rigorous style and is a pleasure to read.' Jacek Banasiak, University of Pretoria

• Introduction; 1. Complete metric spaces; 2. Banach's principle; 3. Picard's theorem; 4. Banach spaces; 5. Renewal equation in the McKendrick–von Foerster model; 6. Riemann integral for vector-valued functions; 7. The Stone–Weierstrass theorem; 8. Norms do differ; 9. Hilbert spaces; 10. Complete orthonormal sequences; 11. Heat equation; 12. Completeness of the space of operators; 13. Working in L(X); 14. The Banach–Steinhaus theorem and strong convergence; 15. We go deeper, deeper we go (into the structure of complete spaces); 16. Semigroups of operators; Appendix. Two consequences of the Hahn–Banach theorem; References; Index.