[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