499 research outputs found
Representations for Moore-Penrose inverses in Hilbert spaces
AbstractLet H1, H2 be two Hilbert spaces, and let T : H1 → H2 be a bounded linear operator with closed range. We present some representations of the perturbation for the Moore-Penrose inverse in Hilbert spaces for the case that the perturbation does not change the range or the null space of the operator
The product of operators with closed range in Hilbert C*-modules
Suppose and are bounded adjointable operators with close range
between Hilbert C*-modules, then has closed range if and only if
is an orthogonal summand, if and only if is
an orthogonal summand. Moreover, if the Dixmier (or minimal) angle between
and is positive and is an orthogonal summand then has closed range.Comment: 12 pages, abstract was changed, accepte
Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law
When improving results about generalized inverses, the aim often is to do
this in the most general setting possible by eliminating superfluous
assumptions and by simplifying some of the conditions in statements. In this
paper, we use Hartwig's well-known triple reverse order law as an example for
showing how this can be done using a recent framework for algebraic proofs and
the software package OperatorGB. Our improvements of Hartwig's result are
proven in rings with involution and we discuss computer-assisted proofs that
show these results in other settings based on the framework and a single
computation with noncommutative polynomials
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