No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

In this paper we study the asymptotics of the discrete spectrum in the gap (−1, 1) of the perturbed Dirac operator$D$(α)=$D$_{0}−α$V$1 acting in$L$_{2}($R$^{3};$C$^{4}) with large coupling constant α. In particular some “non-standard” asymptotic formulae are obtained.

We prove that if$T$is a strictly singular one-to-one operator defined on an infinite dimensional Banach space$X$, then for every infinite dimensional subspace$Y$of$X$there exists an infinite dimensional subspace$Z$of$X$such that$Z∩Y$is infinite dimensional,$Z$contains orbits of$T$of every finite length and the restriction of$T$to$Z$is a compact operator.