The objects of chief interest in the study of a Hilbert space are not the vectors in the space, but the operators on it. Most people who say they study the theory of Hilbert spaces in fact study operator theory. The reason is that the algebra and geometry of vectors, linear functional, quadratic forms, subspaces, and the like are easier than operator theory and are pretty well worked out. Some of these easy and known things are useful and some are amusing; perhaps some are both.
KeywordsHilbert Space Quadratic Form Finite Subset Open Unit Disc Infinite Subset
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