Opuscula Math. 33, no. 3 (2013), 419-438

Opuscula Mathematica

On the decomposition of families of quasinormal operators

Zbigniew Burdak

Abstract. The canonical injective decomposition of a jointly quasinormal family of operators is given. Relations between the decomposition of a quasinormal operator T and the decomposition of a partial isometry in the polar decomposition of T are described. The decomposition of pairs of commuting quasinormal partial isometries and its applications to pairs of commuting quasinormal operators is shown. Examples are given.

Keywords: multiple canonical decomposition, quasinormal operators, partial isometry.

Mathematics Subject Classification: 47B20, 47A45.

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  • Zbigniew Burdak
  • University of Agriculture, Department of Applied Mathematics, ul. Balicka 253c, 30-198 Krakow, Poland
  • Received: 2012-07-17.
  • Revised: 2013-02-07.
  • Accepted: 2013-02-18.
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Cite this article as:
Zbigniew Burdak, On the decomposition of families of quasinormal operators, Opuscula Math. 33, no. 3 (2013), 419-438, http://dx.doi.org/10.7494/OpMath.2013.33.3.419

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