Illinois Journal of Mathematics

Holomorphic functional calculus on upper triangular forms in finite von Neumann algebras

K. Dykema, F. Sukochev, and D. Zanin

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Abstract

The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup–Schultz hyperinvariant projections, behave well with respect to holomorphic functional calculus.

Article information

Source
Illinois J. Math., Volume 59, Number 3 (2015), 819-824.

Dates
Received: 1 June 2016
Revised: 7 June 2016
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1475266410

Digital Object Identifier
doi:10.1215/ijm/1475266410

Mathematical Reviews number (MathSciNet)
MR3554235

Zentralblatt MATH identifier
1353.47076

Subjects
Primary: 47C15: Operators in $C^*$- or von Neumann algebras

Citation

Dykema, K.; Sukochev, F.; Zanin, D. Holomorphic functional calculus on upper triangular forms in finite von Neumann algebras. Illinois J. Math. 59 (2015), no. 3, 819--824. doi:10.1215/ijm/1475266410. https://projecteuclid.org/euclid.ijm/1475266410


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References

  • L. G. Brown, Lidskii's theorem in the type II case, Geometric methods in operator algebras (Kyoto, 1983), vol. 123, Longman Sci. Tech., Harlow, 1986, pp. 1–35.
  • K. Dykema, F. Sukochev and D. Zanin, A decomposition theorem in II$_1$-factors, J. Reine Angew. Math. 708 (2015), 97–114.
  • U. Haagerup and H. Schultz, Invariant subspaces for operators in a general II$_1$-factor, Publ. Math. Inst. Hautes Études Sci. 109 (2009), 19–111.