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Semigroups of Partial Isometries and Symmetric Operators

✍ Scribed by R. T. W. Martin

Publisher: SP Birkhäuser Verlag Basel
Year: 2011
Tongue: English
Weight: 344 KB
Volume: 70
Category: Article
ISSN: 0378-620X
DOI: 10.1007/s00020-011-1878-z

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If S (n ,m ) (n ,m )≥(0, 0) is a multiplicative family of partial isometries on Z 2 with the lexicographic order, then S (1, 0) and S (0, 1) commute in a certain weak sense. Let A and B be commuting unitary extensions of S (1, 0) and S (0, 1) . We give a sufficient condition for A n B m (n ,m )∈Z 2