In this paper, we continue our study of the norm-closure of the set CE of bounded linear
operators acting on a complex, infinite-dimensional, separable Hilbert space H which may …

We prove that, by assuming the existence of at least one left upper semi-Fredholm operator,
then under some natural conditions, the singular operator equation AX− XB= C is solvable if …

Let $\mathcal {H} $ be a complex, separable Hilbert space, and set $\mathfrak {c}($ NIL $
_2)=\{MN-NM: N, M\in\mathcal {B}(\mathcal {H}), M^ 2= 0= N^ 2\} $. When $\dim\,\mathcal …

We describe the norm-closures of the set $\mathfrak {C} _ {\mathfrak {E}} $ of commutators of
idempotent operators and the set $\mathfrak {E}-\mathfrak {E} $ of differences of idempotent …

Let T be a bounded linear operator on a complex Hilbert space H. We present some
necessary and sufficient conditions for T to be the generalized pencil P+ α Q+ β PQ of a pair …

1 Introduction Page 1 Nihonkai Math. J. Vol.15(2004), 93-99 Commutators of Orthogonal
Projections Qihui Li Abstract In this note we prove that a bounded linearoperator $T$ on a …

Let T be an operator on a Banach space X that is similar to− T via an involution U. Then, U
decomposes the Banach space X as X= X 1⊕ X 2 with respect to which decomposition we …

We show that the spectral radius algebras of certain quadratic operators possess nontrivial
invariant subspaces. Additionally, such algebras properly contain the operator's commutant …

In this paper, we characterize the idempotency, the invertibility or generalized invertibility,
the positivity and the range relations of the commutator C= PQ-QP and the anticommutator …

Singular Sylvester equation and its applications Page 1 University of Niš Faculty of
Sciences and Mathematics Bogdan D. -Dordevic Singular Sylvester equation and its …