On the Polar Decomposition of the Product of Two Operators and Its Applications |
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| Authors: | Masatoshi Ito Takeaki Yamazaki Masahiro Yanagida |
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| Affiliation: | (1) Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, Tokyo, 162-8601, Japan;(2) Department of Mathematics, Kanagawa University, Yokohama, 221-8686, Japan |
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| Abstract: | Let T = U|T| and S = V|S| be the polar decompositions. In thispaper, we shall obtain the polar decomposition of TS as TS = UWV|TS|,where |T||S*| = W||T||S*|| is the polar decomposition.Next, we shall show that TS = UV|TS| is the polar decomposition ifand only if |T| commutes with |S*|.Lastly, we shall apply this result to binormal and centered operators.We shall obtain characterizations of these operator classes from the viewpointof the polar decomposition. |
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| Keywords: | 47A05 47B20 |
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