“Zur algebra der funktionaloperationen und theorie der normalen operatoren.” Offprint from Mathematische Annalen, Vol. 102, No. 3, pp. 370-427
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- Berlin: Julius Springer, 1929
Berlin: Julius Springer, 1929. Original printed wrappers. An excellent copy. First printing, the first introduction of Von Neumann’s “Algebra of functional operations and theory of normal operators,” thereafter referred to as Von Neumann algebras. This is von Neumann’s paper on the spectral theorem for normal operators, with detailed discussion of the weakly closed *-subalgebra generated by a set of operators
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann was motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. Von Neumann saw two motivating forces behind the study of these algebras: applications to the newly emergent quantum physics, and application to the study of infinite groups. Quantum physics, as it was being formulated, was involved with algebraic combinations operators. It was certain to require (at the mathematical level) a deeper understanding of the structure of algebras of operators. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. The technique of group algebras had been so useful in the study of finite groups that some corresponding construct for infinite groups was certain to be crucial for their analysis.
Von Neumann algebras have found applications in diverse areas of mathematics like knot theory, statistical mechanics, quantum field theory, local quantum physics, free probability, noncommutative geometry, representation theory, differential geometry, and dynamical systems.
Von Neumann (1903-1957), one of the most brilliant logicians and mathematical analysts of the century, was an original and creative thinker whose research was carried out in the vast and complex fields of both pure and applied mathematics. In particular, he concentrated his ingenious talents on the study of analysis and combinatorics and conducted important investigations into various aspects of logic and automata which had a profound influence on the development of the present day computer.
See https://en.wikipedia.org/wiki/Von_Neumann_algebra.
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann was motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. Von Neumann saw two motivating forces behind the study of these algebras: applications to the newly emergent quantum physics, and application to the study of infinite groups. Quantum physics, as it was being formulated, was involved with algebraic combinations operators. It was certain to require (at the mathematical level) a deeper understanding of the structure of algebras of operators. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. The technique of group algebras had been so useful in the study of finite groups that some corresponding construct for infinite groups was certain to be crucial for their analysis.
Von Neumann algebras have found applications in diverse areas of mathematics like knot theory, statistical mechanics, quantum field theory, local quantum physics, free probability, noncommutative geometry, representation theory, differential geometry, and dynamical systems.
Von Neumann (1903-1957), one of the most brilliant logicians and mathematical analysts of the century, was an original and creative thinker whose research was carried out in the vast and complex fields of both pure and applied mathematics. In particular, he concentrated his ingenious talents on the study of analysis and combinatorics and conducted important investigations into various aspects of logic and automata which had a profound influence on the development of the present day computer.
See https://en.wikipedia.org/wiki/Von_Neumann_algebra.
Details
Title
“Zur algebra der funktionaloperationen und theorie der normalen operatoren.” Offprint from Mathematische Annalen, Vol. 102, No. 3, pp. 370-427
Author
VON NEUMANN, John
Condition
Unknown
Publisher
Julius Springer: Berlin
Date
1929