## $$m$$-isometric operators on Banach spaces.(English)Zbl 1197.47008

Partial isometries, extending the notion of isometry, have played a significant role in the study of Hilbert space operators; J. Agler and M. Stankus [Integral Equations Oper. Theory 21, 383–429 (1995; Zbl 0836.47008)] studied $$m$$-isometries on Hilbert space. The authors’ aim in the present work is to introduce the notion of $$m$$-isometric operator on Banach spaces and to study some basic properties of this class of operators. They generalize the results of Agler–Stankus and describe the spectal picture of $$m$$-isometries.

### MSC:

 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

### Keywords:

$$m$$-isometry; $$m$$-invertibility; spectrum; partial isometry

Zbl 0836.47008
Full Text:

### References:

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