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On the Polar Decomposition of the Product of Two Operators and Its Applications

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Abstract.

Let T = U|T| and S = V|S| be the polar decompositions. In this paper, 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 if and 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 viewpoint of the polar decomposition.

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Authors and Affiliations

  1. Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, Tokyo, 162-8601, Japan

    Masatoshi Ito & Masahiro Yanagida

  2. Department of Mathematics, Kanagawa University, Yokohama, 221-8686, Japan

    Takeaki Yamazaki

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  1. Masatoshi Ito
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  2. Takeaki Yamazaki
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  3. Masahiro Yanagida
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Correspondence to Masatoshi Ito, Takeaki Yamazaki or Masahiro Yanagida.

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Ito, M., Yamazaki, T. & Yanagida, M. On the Polar Decomposition of the Product of Two Operators and Its Applications. Integr. equ. oper. theory 49, 461–472 (2004). https://doi.org/10.1007/s00020-002-1215-7

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  • DOI: https://doi.org/10.1007/s00020-002-1215-7

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