(m, q)-ISOMETRIES ON METRIC SPACES

(m, q)-ISOMETRIES ON METRIC SPACES

We show that there exist a linear m-isometry on a Hilbert space which is not continuous, and a continuous m-isometry on a Hilbert space which is not affine. Further we define (m, q)-isometries on metric spaces and prove their basic properties.

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Veröffentlicht in:Journal of operator theory 2014-12, Vol.72 (2), p.313-328
Hauptverfasser: Bermudez, Teresa, Martinon, Antonio, Muller, Vladimir
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Differential equations
Hilbert spaces
Integers
Linear algebra
Linear transformations
Mathematical theorems
Normed spaces
Operator theory
Real numbers
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Zusammenfassung:We show that there exist a linear m-isometry on a Hilbert space which is not continuous, and a continuous m-isometry on a Hilbert space which is not affine. Further we define (m, q)-isometries on metric spaces and prove their basic properties.
ISSN:0379-4024
1841-7744
DOI:10.7900/jot.2013jan29.1996