16 citations · 18 across the 5 of their papers we have counts for
8 papers
Strictly semi-transitive operator algebras
H. P. Rosenthal, V. G. Troitsky
An algebra A of operators on a Banach space X is called strictly semi-transitive if for all non-zero x,y in X there exists an operator S in A such that Sx=y or Sy=x. We show that i…
Minimal vectors in arbitrary Banach spaces
Vladimir G. Troitsky
We extend the method of minimal vectors to arbitrary Banach spaces. It is proved, by a variant of the method, that certain quasinilpotent operators on arbitrary Banach spaces have…
Measures of non-compactness of operators on Banach lattices
Vladimir G. Troitsky
Andreu et al [2] and Sadovskii [11] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop re…
A theorem of Krein revisited
Timur Oikhberg, Vladimir G. Troitsky
M. Krein proved in 1948 that if T is a continuous operator on a normed space leaving invariant an open cone, then its adjoint T* has an eigenvector. We present generalizations of t…
Spectrum of a weakly hypercyclic operator meets the unit circle
S. J. Dilworth, Vladimir G. Troitsky
It is shown that every component of the spectrum of a weakly hypercyclic operator meets the unit circle. The proof is based on the lemma that a sequence of vectors in a Banach spac…
On quasi-affine transforms of Read's operator
Thomas Schlumprecht, Vladimir G. Troitsky
We show that C.J.Read's example of an operator T on l_1 which does not have any non-trivial invariant subspaces is not the adjoint of an operator on a predual of l_1. Furthermore,…