Preliminaries and notation
The prerequisites for a thorough understanding of this essentially selfcontained exposition are quite modest. Rather than to write a small textbook on these, or go to the other extreme and say that these are well known and may be easily found in the literature, some sort of a middle road seems to offer a more satisfactory solution. We state a sufficient number of references and merely redefine a few notions, some of which, though not overemphasized in standard texts, play an important part in our discussion. We also reconstruct the proof of the “polar decomposition” for operators which indeed plays a central role in this exposition.
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