On normal operator logarithms
Let X,Y be normal bounded operators on a Hilbert space such that e X=eY. If the spectra of X and Y are contained in the strip S of the complex plane defined by |I(z)|≤π, we show that |X|=|Y|. If Y is only assumed to be bounded, then |X|Y=Y|X|. We give a formula for X-Y in terms of spectral projectio...
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2013
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/85121 |
| Aporte de: |
| id |
I19-R120-10915-85121 |
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dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Exponential map Normal operator Spectral theorem |
| spellingShingle |
Matemática Exponential map Normal operator Spectral theorem Chiumiento, Eduardo Hernán On normal operator logarithms |
| topic_facet |
Matemática Exponential map Normal operator Spectral theorem |
| description |
Let X,Y be normal bounded operators on a Hilbert space such that e X=eY. If the spectra of X and Y are contained in the strip S of the complex plane defined by |I(z)|≤π, we show that |X|=|Y|. If Y is only assumed to be bounded, then |X|Y=Y|X|. We give a formula for X-Y in terms of spectral projections of X and Y provided that X,Y are normal and e X=eY. If X is an unbounded self-adjoint operator, which does not have (2k+1)π,k∈ℤ, as eigenvalues, and Y is normal with spectrum in S satisfying eiX=eY, then Y∈{ e iX}″. We give alternative proofs and generalizations of results on normal operator exponentials proved by Schmoeger. |
| format |
Articulo Articulo |
| author |
Chiumiento, Eduardo Hernán |
| author_facet |
Chiumiento, Eduardo Hernán |
| author_sort |
Chiumiento, Eduardo Hernán |
| title |
On normal operator logarithms |
| title_short |
On normal operator logarithms |
| title_full |
On normal operator logarithms |
| title_fullStr |
On normal operator logarithms |
| title_full_unstemmed |
On normal operator logarithms |
| title_sort |
on normal operator logarithms |
| publishDate |
2013 |
| url |
http://sedici.unlp.edu.ar/handle/10915/85121 |
| work_keys_str_mv |
AT chiumientoeduardohernan onnormaloperatorlogarithms |
| bdutipo_str |
Repositorios |
| _version_ |
1764820488986558464 |