IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
On normal operator logarithms
Autor/es:
CHIUMIENTO EDUARDO
Revista:
LINEAR ALGEBRA AND ITS APPLICATIONS
Editorial:
ELSEVIER SCIENCE INC
Referencias:
Lugar: Amsterdam; Año: 2013 vol. 439 p. 455 - 455
ISSN:
0024-3795
Resumen:
Let X,Y be normal bounded operators on a Hilbert space such that e^X=e^Y.  If the spectra of X and Y are contained in the  strip S of the complex plane defined by |Im(z)|leq pi, 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=e^Y. If X is an unbounded self-adjoint operator, which does not have  (2k+1) pi, k in Z,  as eigenvalues, and Y is normal with spectrum in S satisfying e^{iX}=e^Y, then Y in {  e^{iX} }ยดยด. We  give alternative proofs and generalizations of results on normal operator exponentials proved by Ch. Schmoeger.