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Unitary extensions of partial isometries

✍ Scribed by Nieves Amoretti; Marisela Domínguez

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
139 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 to be a unitary extension of the given family. Under this condition we present a description of the set of extensions.

We also describe the set of all minimal commuting unitary extensions of any pair of partial isometries that commutes in the same weak sense that S (1, 0) and S (0, 1) commute.

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