Commutators and normal operators
Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 197-198
Voir la notice de l'article provenant de la source Cambridge University Press
Let X be a Banach space and L(X) the Banach algebra of bounded linear operators on X. An operator T in L(X) is hermitian if ∥eitT∥ = 1 (t ∈ R), and is normal if T = R + iJ where R and J are commuting normal operators; R and J are then determined uniquely by T, and we may write T* = R–iJ. These definitions extend those for operators on Hilbert spaces. More details may be found in [1].
Crabb, M. J.; Spain, P. G. Commutators and normal operators. Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 197-198. doi: 10.1017/S001708950000327X
@article{10_1017_S001708950000327X,
author = {Crabb, M. J. and Spain, P. G.},
title = {Commutators and normal operators},
journal = {Glasgow mathematical journal},
pages = {197--198},
year = {1977},
volume = {18},
number = {2},
doi = {10.1017/S001708950000327X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000327X/}
}
[1] 1.Bonsall, F. F. and Duncan, J., Complete normed algebras (Springer-Verlag, 1973). Google Scholar | DOI
[2] 2.Dowson, H. R., Gillespie, T. A. and Spain, P. G., A commutativity theorem for hermitian operators, Math. Ann. 220 (1976), 215–217. Google Scholar | DOI
[3] 3.Palmer, T. W., Unbounded normal operators on Banach spaces, Trans. Amer. Math. Soc. 133 (1968), 385–414. Google Scholar | DOI
[4] 4.Putnam, C. R., On normal operators in Hilbert space, Amer. J. Math. 73 (1951), 357–362. Google Scholar | DOI
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