## Direct summands of systems of continuous linear transformations |

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### Contents

Introduction | 5 |

Characterizations of split monomorphisms | 19 |

The broken chain condition for Csystems | 32 |

Copyright | |

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### Common terms and phrases

abelian groups action algebraic Cv-system algebraic system automorphism Banach bifunctor bijection Borsuk CA'-system cardinal numbers chain diagram chain of type CN-system commutativity condition continuous linear maps continuous linear transformations decomposition defined denote direct sum direct summand directed set DISSERTATIONES MATHEMATICAE e e CN e e CN acts End(X endomorphism equations equivalent fc-l finest weak topologies finite-dimensional and indecomposable finite-dimensional indecomposable finite-dimensional subsystem functor gniadeckich Hence Hilbert space Hom(X homomorphism p,y homon1orphism horn and tensor isomorphism types left inverse Lemma linear functional linear isomorphism linearly independent locally convex space Math morphism pairs of linear Proof Proposition QD(V QD{V Section separated locally convex sequences split monomorphism subsystem G summand of type tensor product tensor relations Theorem 4.5 theory topological linear isomorphism topological systems topological vector spaces type 77 WARSZAWA Pologne y>jk zero trace