16 citations · 18 across the 6 of their papers we have counts for
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math.FA2002
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…
math.FA2002
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…
math.FA2002★ 2 cited
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…