Similar operators
From Encyclopedia of Mathematics
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:
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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
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