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1
Content available remote

Invariant Subspaces and Spectral Conditions on Operator Semigroups

100%
Radjavi H.
Banach Center Publications
|
1997
|
tom 38
|
nr 1
287-296
2
Content available remote

Linear maps preserving quasi-commutativity

64%
Radjavi H., Šemrl P.
Studia Mathematica
|
2008
|
tom 184
|
nr 2
191-204
EN
Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.
3
Content available remote

Universal bounds for positive matrix semigroups

51%
Livshits L., MacDonald G., Marcoux L., Radjavi H.
Studia Mathematica
|
2016
|
tom 232
|
nr 2
143-153
EN
We show that any compact semigroup of positive n × n matrices is similar (via a positive diagonal similarity) to a semigroup bounded by √n. We give examples to show this bound is best possible. We also consider the effect of additional conditions on the semigroup and obtain improved bounds in some cases.
4
Content available remote

Universal bounds for matrix semigroups

51%
Livshits L., MacDonald G., Radjavi H.
Studia Mathematica
|
2011
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tom 203
|
nr 1
69-77
EN
We show that any compact semigroup of n × n matrices is similar to a semigroup bounded by √n. We give examples to show that this bound is best possible and consider the effect of the minimal rank of matrices in the semigroup on this bound.
5
Content available remote

A perturbation characterization of compactness of self-adjoint operators

51%
Radjavi H., Tam P.-K., Tan K.-K.
Studia Mathematica
|
2003
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tom 158
|
nr 3
199-205
EN
A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.
6
Content available remote

Mean ergodicity for compact operators

51%
Radjavi H., Tam P.-K., Tan K.-K.
Studia Mathematica
|
2003
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tom 158
|
nr 3
207-217
EN
A mean ergodic theorem is proved for a compact operator on a Banach space without assuming mean-boundedness. Some related results are also presented.
7
Content available remote

On operator bands

39%
Drnovšek R., Livshits L., MacDonald G. W., Mathes B., Radjavi H., Šemrl P.
Studia Mathematica
|
2000
|
tom 139
|
nr 1
91-100
EN
A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K>1 there exists an irreducible operator band on the Hilbert space $l^2$ which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each member has operator norm equal to 1. Given a positive integer r, we introduce a notion of weak r-transitivity of a set of bounded operators on a Banach space. We construct an operator band on $l^2$ that is weakly r-transitive and is not weakly (r+1)-transitive. We also study operator bands S satisfying a polynomial identity p(A, B) = 0 for all non-zero A,B ∈ S, where p is a given polynomial in two non-commuting variables. It turns out that the polynomial $p(A, B) = (A B - B A)^2$ has a special role in these considerations.
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