Dilations and Commutant Lifting for Jointly Isometric Operators—A Geometric Approach

✍ Scribed by K.R.M. Attele; A.R. Lubin

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 423 KB
• Volume: 140
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.0109

✦ Synopsis

A tuple of commuting contractions T=(T 1 , T 2 , ..., T n ) is called a joint-isometry if T* j T j =I. We give a geometric proof that joint isometries have a regular unitary dilation and that its commutant lifts. We also show that T is subnormal and that its minimal normal extension is also jointly isometric.

1996 Academic Press, Inc.

for all choices of integers n i 0, i=1, ..., r and for every finite set of subscripts j i # J, where P denotes the orthogonal projection of K onto H. The article no.