… Such operators (matrices) were introduced and … a compatible range (CoR) operator if T and
T∗ coincide on R(T) ∩ R(T∗). We extend and improve some results about DR operators and …

… in has kernel : by point (a) of Lemma 3.3, we find that maps every rank operator to a vector
of its range provided that this range differs from . Now, denote by the map that is attached to in …

… Let T be a bounded linear operator with a one-dimensional range from Y into … operator will
be used only for bounded linear operators. Let ZY be Banach spaces and let Τ be an operator …

… range-compatible group homomorphisms. The motivation for doing so is twofold: firstly,
range-compatible … of all range-compatible semi-linear maps on large operator spaces. In this …

… operator with real numerical range to have a self conjugate closure. Self conjugate operators
R … with respect to every semi-inner-product compatible with the norm of N. We shall use this …

… kernel and range, respectively. As in [2], we say that A ∈ [H] is a compatible range operator
(CoR … This requirement is satisfied vacuously if A is a DR operator, ie, R(A) ∩ R(A∗) = {0}, or …

… [3] for locally linearly dependent triples of linear operators, a theorem which is now known to
… our own classification of range-compatible linear maps over large operator spaces. Before …

… range. Following the terminology of Gohberg and Zambickiı, we say that a bounded operator
on E is a proper operator if … class operators and L is the space of Hilbert-Schmidt operators, …

… A closed subspace S of H and a positive semidefinite operator A are called compatible if …
In [9], the compatibility of a pair (A, S) is related to the existence in the operator range R(A1/2) of …

… } such that W contains no operator with range K f 1 ⋆ , and then we apply the result once
more to find some f 2 ⋆ ∈ U ⋆ ∖ K f 1 ⋆ such that W contains no operator with range K f 2 ⋆ . □ …