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mathematics, the Brown measure of an operator in a finite
factor is a
probability measure on the complex plane which may be viewed as an analog of the
spectral counting measure (based on
algebraic multiplicity) of matrices.
It is named after
Lawrence G. Brown.
Let be a finite factor with the canonical normalized trace and let be the identity operator. For every operator the function
sense is a probability measure on
which is called the Brown measure of
Here the Laplace operator
The subharmonic function can also be written in terms of the
Fuglede−Kadison determinant as follows
Direct integral – generalization of the concept of direct sumPages displaying wikidata descriptions as a fallback
- Brown, Lawrence (1986), "Lidskii's theorem in the type case", Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow, 123: 1–35. Geometric methods in operator algebras (Kyoto, 1983).