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

Sid Ahmed, Ould Ahmed Mahmoud

Asian-Eur. J. Math. 3, No. 1, 1-19 (2010).

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.

Reviewer: V. Lokesha (Bangalore)

MSC:

47A05

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

Keywords:

\(m\)-isometry; \(m\)-invertibility; spectrum; partial isometry

Citations:

Zbl 0836.47008

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