Adjoint functors induced by adjoint linear transformations
Author: Paul H. Palmquist
Journal: Proc. Amer. Math. Soc. 44 (1974), 251-254
MSC: Primary 46M15; Secondary 18A40
MathSciNet review: 0346548
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Abstract: Adjoint linear transformations between Hilbert spaces or, more generally, between dual systems of topological vector spaces induce contravariant functors which are adjoint on the right—essentially a Galois connection between the posets of subsets (or subspaces) of the spaces. Modulo scalars the passage from linear maps to functors is one-to-one; indeed, modulo scalars, two linear transformations are adjoint (hence both are weak continuous) if and only if the induced functors are adjoint.
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Keywords: Adjoint, adjoint linear operators, adjoint functors, adjoint on the right, Galois connection, Hilbert space, poset, topological vector space, dual system
Article copyright: © Copyright 1974 American Mathematical Society