Extension of Spectral Scales to Unbounded Operators
We extend the notion of a spectral scale to n-tuples of unbounded operators affiliated with a finite von Neumann Algebra. We focus primarily on the single-variable case and show that many of the results from the bounded theory go through in the unbounded situation. We present the currently available...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/713563 |
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| _version_ | 1832551373746470912 |
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| author | M. D. Wills |
| author_facet | M. D. Wills |
| author_sort | M. D. Wills |
| collection | DOAJ |
| description | We extend the notion of a spectral scale to n-tuples of unbounded
operators affiliated with a finite von Neumann Algebra. We focus primarily
on the single-variable case and show that many of the results from the bounded
theory go through in the unbounded situation. We present the currently available material on the unbounded multivariable situation. Sufficient conditions
for a set to be a spectral scale are established. The relationship between convergence of operators and the convergence of the corresponding spectral scales
is investigated. We establish a connection between the Akemann et al. spectral scale (1999) and that of Petz (1985). |
| format | Article |
| id | doaj-art-11cb2823d66d476dae996354d41f34ef |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-11cb2823d66d476dae996354d41f34ef2025-02-03T06:01:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/713563713563Extension of Spectral Scales to Unbounded OperatorsM. D. Wills0Department of Mathematics, Weber State University, Ogden, UT 84404, USAWe extend the notion of a spectral scale to n-tuples of unbounded operators affiliated with a finite von Neumann Algebra. We focus primarily on the single-variable case and show that many of the results from the bounded theory go through in the unbounded situation. We present the currently available material on the unbounded multivariable situation. Sufficient conditions for a set to be a spectral scale are established. The relationship between convergence of operators and the convergence of the corresponding spectral scales is investigated. We establish a connection between the Akemann et al. spectral scale (1999) and that of Petz (1985).http://dx.doi.org/10.1155/2010/713563 |
| spellingShingle | M. D. Wills Extension of Spectral Scales to Unbounded Operators International Journal of Mathematics and Mathematical Sciences |
| title | Extension of Spectral Scales to Unbounded Operators |
| title_full | Extension of Spectral Scales to Unbounded Operators |
| title_fullStr | Extension of Spectral Scales to Unbounded Operators |
| title_full_unstemmed | Extension of Spectral Scales to Unbounded Operators |
| title_short | Extension of Spectral Scales to Unbounded Operators |
| title_sort | extension of spectral scales to unbounded operators |
| url | http://dx.doi.org/10.1155/2010/713563 |
| work_keys_str_mv | AT mdwills extensionofspectralscalestounboundedoperators |