Model
Digital Document
Publisher
Florida Atlantic University
Description
An operator acting on a Banach space is called an isometry if it preserves the norm of the space. An interesting problem is to determine the form or structure of linear isometries on Banach spaces. This can be done in some instances.
This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear isometries have the form of a permutation of the elements of the sequences in the given space, with each component of each sequence multiplied by a complex number of absolute value 1.
This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear isometries have the form of a permutation of the elements of the sequences in the given space, with each component of each sequence multiplied by a complex number of absolute value 1.
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