In this paper we study the general concept of reduced solution for a Douglas type equation
and we parametrize these solutions using generalized inverses. On the other hand, we …

We extend in this paper the notion of Cauchy dual to operators with closed range. We then
give several useful properties of Cauchy duals extending the case of left-invertible …

Let H be a complex Hilbert space and let B (H) be the algebra of all bounded linear
operators on H. In this paper, for T∈ B (H) and a unit vector x∈ H, we introduce a local …

Abstract We study the Moore–Penrose inverse of perturbations by a proper symmetrically-
normed ideal of a closed range operator on a Hilbert space. We show that the notion of …

We obtain some results related to the problems of Badea and Mbekhta (2005)[1] concerning
the similarity to partial isometries using the generalized inverses. Especially, we involve the …

A note on modular frames for closed range operators in Hilbert $$\mathcal {C}^{*}$$ -modules
| Rendiconti del Circolo Matematico di Palermo Series 2 Skip to main content SpringerLink …

Let $\mathcal {H} $ be a separable infinite-dimensional complex Hilbert space and let
$\mathcal {J} $ be a two-sided ideal of the algebra of bounded operators $\mathcal …

We define a new metric on the set of all closed linear operators between Hilbert spaces and
investigate its properties. In particular, we show that the set of all closed operators with a …

We study the set XX of split operators acting in the Hilbert space HH: X={T ∈ B (H): N (T) ∩
R (T)={0\}{\rm and\N (T)+ R (T)= H\}. X= T∈ B (H): N (T)∩ R (T)= 0 and N (T)+ R (T)= H …

To every bounded linear operator A between Hilbert spaces 𝓗 and 𝒦 three cardinals lr (A), li
(A) and lf (A) and a binary number lb (A) are assigned in terms of which the descriptions of …