Pedersen–Takesaki operator equation and operator equation AX = B in Hilbert C⁎-modules

<p>In this manuscript, the notion of absolutely invertible was extended consistently from semi-normed rings to the class of general topological rings. Then, the closure of the absolutely invertibles multiplied by a certain element was proved to be contained in the set of topological divisors of the element. Also, a sufficient condition for the closed unit ball of a complete unital normed ring to become a closed unit neighborhood of zero was found. Finally, two applications to classical operator theory were provided, i.e., every Banach space of dimension of at least $ 2 $ could be equivalently re-normed in such a way that the group of surjective linear isometries was not a normal subgroup of the group of isomorphisms, and every infinite-dimensional Banach space, containing a proper complemented subspace isomorphic to it, could be equivalently re-normed so that the set of surjective linear operators was not dense in the Banach algebra of bounded linear operators.</p>

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Pedersen–Takesaki operator equation and operator equation AX = B in Hilbert C⁎-modules

Cited by 3 publications

References 15 publications

On the solution of nonlinear operator equations and the invariant subspace

On the solution of nonlinear operator equations and the invariant subspace

Characterizations of generalized pencils of pairs of projections

On absolutely invertibles

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Pedersen–Takesaki operator equation and operator equation AX = B in Hilbert C⁎-modules

Cited by 3 publications

References 15 publications

On the solution of nonlinear operator equations and the invariant subspace

On the solution of nonlinear operator equations and the invariant subspace

Characterizations of generalized pencils of pairs of projections

On absolutely invertibles

Contact Info

Product

Resources

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Pedersen–Takesaki operator equation and operator equation AX = B in Hilbert C⁎-modules