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On n-quasi-m-isometric operators
Preview AbstractWe introduce the class of n-quasi-m-isometric operators on Hilbert space. This generalizes the class of m-isometric operators on Hilbert space introduced by Agler and Stankus. An operator T∈B(H) is said to be n-quasi-m-isometric if
T∗n(m∑k=0(−1)k(mk)T∗m−kTm−k)Tn=0.In this paper 2×2 matrix representation of a n-quasi-m-isometric operator is given. Using this representation we establish some basic properties of this class of operators.m-ISOMETRIC OPERATORS ON BANACH SPACES
Preview AbstractWe introduce the class of m-isometric operators on Banach spaces. This generalizes to Banach space the m-isometric operators on Hilbert space introduced by Agler and Stankus. We establish some basic properties and we introduce the notion of m-invertibility as a natural generalization of the invertibility on Banach spaces.
(m, p)-isometric and (m, ∞)-isometric operator tuples on normed spaces
Preview AbstractWe generalize the notion of m-isometric operator tuples on Hilbert spaces in a natural way to operator tuples on normed spaces. This is done by defining a tuple analogue of (m, p)-isometric operators, so-called (m, p)-isometric operator tuples. We then extend this definition further by introducing (m, ∞)-isometric operator tuples and study properties of and relations between these objects.