Opuscula Math. 33, no. 3 (2013), 419-438
On the decomposition of families of quasinormal operators
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.
- Received: 2012-07-17.
- Revised: 2013-02-07.
- Accepted: 2013-02-18.