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 |
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2013
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Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/85121 |
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I19-R120-10915-85121 |
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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 |