The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying 181 –
200 of
213
We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin, J. Zemánek...
We study left n-invertible operators introduced in two recent papers. We show how to construct a left n-inverse as a sum of a left inverse and a nilpotent operator. We provide refinements for results on products and tensor products of left n-invertible operators by Duggal and Müller (2013). Our study leads to improvements and different and often more direct proofs of results of Duggal and Müller (2013) and Sid Ahmed (2012). We make a conjecture about tensor products of left n-invertible operators...
A Banach space operator T ∈ has a left m-inverse (resp., an essential left m-inverse) for some integer m ≥ 1 if there exists an operator S ∈ (resp., an operator S ∈ and a compact operator K ∈ ) such that (resp., ). If is left -invertible (resp., essentially left -invertible), then the tensor product T₁ ⊗ T₂ is left (m₁ + m₂-1)-invertible (resp., essentially left (m₁ + m₂-1)-invertible). Furthermore, if T₁ is strictly left m-invertible (resp., strictly essentially left m-invertible), then...
The boundedness properties of commutators for operators are of central importance in Mathematical Analysis, and some of these commutators arise in a natural way from interpolation theory. Our aim is to present a general abstract method to prove the boundedness of the commutator for linear operators and certain unbounded operators that appear in interpolation theory, previously known and a priori unrelated for both real and complex interpolation methods, and also to show how the abstract result...
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
The questions when a derivation on a Jordan-Banach algebra has quasi-nilpotent values, and when it has the range in the radical, are discussed.
We prove that the spaces of (α,β)-derivations on certain operator algebras are topologically reflexive in the weak operator topology. Characterizations of automorphisms and (α,β)-derivations on reflexive algebras are also given.
Currently displaying 181 –
200 of
213