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

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
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Received: 2012-07-17.
Revised: 2013-02-07.
Accepted: 2013-02-18.
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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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