Symmetric functionals and singular traces

P. G. Dodds; B. De Pagter; E. M. Semenov; F. A. Sukochev

doi:10.1023/A:1009720826217

Symmetric functionals and singular traces

P. G. Dodds, B. De Pagter, E. M. Semenov, F. A. Sukochev

College of Science and Engineering

Research output: Contribution to journal › Article › peer-review

48 Citations (Scopus)

Abstract

We study the construction and properties of positive linear functionals on symmetric spaces of measurable functions which are monotone with respect to submajorization. The construction of such functionals may be lifted to yield the existence of singular traces on certain non-commutative Marcinkiewicz spaces which generalize the notion of Dixmier trace.

Original language	English
Pages (from-to)	47-75
Number of pages	29
Journal	Positivity
Volume	2
Issue number	1
DOIs	https://doi.org/10.1023/A:1009720826217
Publication status	Published - Mar 1998

Keywords

Marcinkiewicz space
Singular trace
Symmetric functional
Symmetric operator space

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10.1023/A:1009720826217Licence: In Copyright

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title = "Symmetric functionals and singular traces",

abstract = "We study the construction and properties of positive linear functionals on symmetric spaces of measurable functions which are monotone with respect to submajorization. The construction of such functionals may be lifted to yield the existence of singular traces on certain non-commutative Marcinkiewicz spaces which generalize the notion of Dixmier trace.",

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AB - We study the construction and properties of positive linear functionals on symmetric spaces of measurable functions which are monotone with respect to submajorization. The construction of such functionals may be lifted to yield the existence of singular traces on certain non-commutative Marcinkiewicz spaces which generalize the notion of Dixmier trace.

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KW - Symmetric operator space

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Symmetric functionals and singular traces

Abstract

Keywords

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