[Authors]
 Oleg Reinov; Qaisar Latif

[Title]
 Sur valeurs propres des op\'erateurs $(r,p)$-nucl\'eaires et 
 conditions d'approximation d'ordre $(r,p)$

[AMS Subj-class]
 47B06 (r,p)-nuclear operator, eigenvalue distribution

[Abstract]
 {\bf On eigenvalues of $(r,p)$-nuclear operators and approximation
 properties of order  $(r,p)$}
 We investigate the distribution of eigenvalues of  $(r,p)$-nuclear
 operators, presenting a small part of Fredholm Theory for the
 corresponding ideal $N_{r,p}.$ Introducing a new notion of the
 approximation property, $AP_{r,p}.$ of order $(r,p),$ we give
 different examples, showing that obtained eigenvalues results are
 sharp. For this we use, in particular, examples of spaces without
 the properties $AP_{r,p}.$ As a by-product of our considerations,
 we obtain some examples of non $s$-nuclear operators $(s<1)$ 
 with $s$-niclear adjoints, answering a question %(Problem 10.1 in [2]) 
 of A.  Hinrichs and A. Pietsch.
 Partially, this work presents PhD Thesis of the second author.

[Comments]
 LaTeX, French, 4 pp.

[Contact e-mail]
 orein51@mail.ru