Introduction to Hilbert Space

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Hilbert space has also provided a source for rich ideas in topology. As a metric space, Hilbert space can be considered an infinite-dimensional linear topological space , and important questions related to its topological properties were raised in the first half of the 20th century. Hilbert space. Info Print Cite.

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Written By: Stephan C. See Article History.

Read More on This Topic. These efforts foreshadowed a new area of topology now…. Start Your Free Trial Today.

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Learn More in these related Britannica articles:. These efforts foreshadowed a new area of topology now referred to as infinite-dimensional topology. Another major area of modern interest is set theoretic topology, in which the connection between topological spaces and notions from set theory and logic is studied. Some of the…. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case.

Introduction to Hilbert spaces

Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude.

With respect to the original lectures, the mathematical flavor in all subjects has been enriched.

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Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics. His teaching encompassed topics in quantum mechanics, special relativity, field theory, elementary particle physics, mathematical physics, and functional analysis. He spent an additional three years in Utrecht as an assistant professor of mathematics, teaching mathematics courses across the entire undergraduate spectrum both at Utrecht University and at the affiliated University College Utrecht.


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He is currently a mathematics lecturer at the University of the South Pacific. His research interests lie in the fields of algebraic topology and operad theory, as well as the mathematical foundations of analysis and generalizations of metric spaces. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

Provides a reader-friendly introduction to Hilbert space that will equip the reader for more demanding further study Presents many clarifying examples Builds a pedagogic bridge between the rigorous mathematical style and the more practical perspective of physicists see more benefits.

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