Paul R. Halmos – författare

This concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. "An exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely." — Bulletin of the American Mathematical Society.

Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews: "Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory." --MATHEMATICAL REVIEWS

This concise classic by a well-known master of mathematical exposition has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. Topics include recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. "The material is organized very well and painlessly presented." — Bulletin of the American Mathematical Society.

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics.In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

The book is a complete collection of Paul Halmos's articles written on the subject of algebraic logic (the theory of Boolean functions). Altogether, there are ten articles, which were published between 1954-1959 in eight different journals spanning four countries. The articles appear in an order that allows the reader unfamiliar with the subject to read them without many prerequisites. In particular, the first article in the book is an accessible introduction to algebraic logic.

Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews: "Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory." --MATHEMATICAL REVIEWS