Adjoint functors induced by adjoint linear transformations
HTML articles powered by AMS MathViewer
- by Paul H. Palmquist PDF
- Proc. Amer. Math. Soc. 44 (1974), 251-254 Request permission
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.References
- Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240 P. Halmos, Introduction to Hilbert spaces, 2nd ed., Chelsea, New York, 1957.
- Reports of the Midwest Category Seminar. IV, Lecture Notes in Mathematics, Vol. 137, Springer-Verlag, Berlin-New York, 1970. Edited by S. MacLane. MR 0263888
- Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 251-254
- MSC: Primary 46M15; Secondary 18A40
- DOI: https://doi.org/10.1090/S0002-9939-1974-0346548-4
- MathSciNet review: 0346548