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On reflexive subobject lattices and reflexive endomorphism algebras

Dong Sheng Zhao (2003)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.

On reflexivity and hyperreflexivity of some spaces of intertwining operators

Michal Zajac (2008)

Mathematica Bohemica

Let T , T ' be weak contractions (in the sense of Sz.-Nagy and Foiaş), m , m ' the minimal functions of their C 0 parts and let d be the greatest common inner divisor of m , m ' . It is proved that the space I ( T , T ' ) of all operators intertwining T , T ' is reflexive if and only if the model operator S ( d ) is reflexive. Here S ( d ) means the compression of the unilateral shift onto the space H 2 d H 2 . In particular, in finite-dimensional spaces the space I ( T , T ' ) is reflexive if and only if all roots of the greatest common divisor of minimal polynomials...

On regularities and Fredholm theory

L. Lindeboom, H. Raubenheimer (2002)

Czechoslovak Mathematical Journal

We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.

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