## Functors on the category of Hilbert spaces |

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### Contents

Duality of functors on H | 1 |

Subfunctors of B and preBanach left ideals | 23 |

Functors on H with FC E H | 58 |

1 other sections not shown

### Common terms and phrases

admissible symmetric bifunctors B(H H Banach ideal Banach left ideal Banach left module Banach sequence ideal bounded linear operators category of Hilbert Cauchy sequence closed graph theorem completion in B(H consequence contravariant functor converges corollary correspondence dense depends naturally dual functor easily seen equivalent example F and G F is isomorphic F is type F on H following holds functor F functor on H given Hence Hilbert space ideal in B(H implies inclusion-map injective isometrical isomorphism left B(E)-module left ideal A,A left invariant crossnorm lemma Let F Let h linear subspace maximal strong Banach metrical isomorphism minimal Banach left morphisms natural transformation normed left ideal operators of rank polar decomposition pre-Banach left ideal pre-Banach left module Proof proposition 1.5.5 proposition 2.3.8 Proposition Let reflexive functors self-dual functors selfadjoint strong Banach left surjective Theorem Let type A functor unitary operator