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Similar operators

From Encyclopedia of Mathematics
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Operators and (not necessarily bounded) on a Banach space for which there exists a bounded operator on having a bounded inverse and such that the following relation applies:

If is a unitary operator, then and are said to be unitarily equivalent.

This concept is an example of the concept of similar mappings. Let and be two mappings of a set into itself. If there is a bijection such that , then these mappings are said to be similar. Attempts have been made to give a definition of similarity for mappings from one set into another ; for example, such mappings are called similar if there exist bijections and of the sets and into themselves such that .

How to Cite This Entry:
Similar operators. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Similar_operators&oldid=48699
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article