[Authors]
 O. I. Reinov

[Title]
 On symmetry of spectra of nuclear operators

[AMS Subj-class]
 47B10 Operators belonging to operator ideals (nuclear, $p$-summing,
       in the Schatten-von Neumann classes, etc.)

[Abstract]
 An optimal criterion for the spectra of nuclear operators in some Banach
 spaces to be central-symmetric is given. In particular, if $X$ is a subspace
 of a quotient of an $L_p(\mu)$-space, $1/s=1+|1/2-1/p|,$ then the spectrum
 of any s-nuclear operator $T$ in $X$ is central-symmetric iff the traces of
 all operators $T, T^3, T^5, ...$ are zero. As a consequence, taking $p=2,$
 we get the corresponding theorem obtained by M. I. Zelikin in 2008 for nuclear
 operators in Hilbert spaces.

[Comments]
 LaTeX, Russian, 4 pp.

[Contact e-mail]
 orein51@mail.ru