It is known that strongly nilpotent matrices over a division ring are linearly triangularizable. We describe the structure of such matrices in terms of the strong nilpotency index. We apply our results on quasi-translation x+H such that JH has strong nilpotency index two.

Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in finite dimensional and infinite dimensional Banach spaces. In addition, we investigate whether approximate spectral mapping conditions (being “close” in some sense) is similarly a su...

In this paper we consider simultaneously triangularizable collections of compact operators and show that similarities of any finite subcollection can be made arbitrarily close to commuting normal operators. As a consequence, we obtain a variant of a theorem of G.-C. Rota. Also, we give some sufficient conditions for simultaneous triangularization of collections of compact operators. Finally, se...

We show that a Jordan algebra of compact quasinilpotent operators which contains a nonzero trace class operator has a common invariant subspace. As a consequence of this result, we obtain that a Jordan algebra of quasinilpotent Schatten operators is simultaneously triangularizable.

In this paper it is proved that a power linear Keller map of dimension three over a field of characteristic zero is linearly triangularizable. Let K be a field. A polynomial map F in dimension n over K is an n-tuple (F1, F2, · · · , Fn) of polynomials in K[X1, X2, · · · , Xn]. If G is another polynomial map of the same dimension, then the composition of F and G is defined by F ◦G = (F1(G1, G2, ...

We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum, and when they satisfy simple trace conditions. In certain cases we show that these co...

in this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. first, we give a generalization of guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. the firs...