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Quasisimilarity of Invariant Subspaces for Uniform Jordan Operators of Infinite Multiplicity

✍ Scribed by Hari Bercovici; Thomas Smotzer

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
666 KB
Volume
140
Category
Article
ISSN
0022-1236

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✦ Synopsis

We show that if T is a uniform Jordan operator of infinite multiplicity, then M is quasisimilar to N if and only if T | M is quasisimilar to T | N and (T * | M = )* is quasisimilar to (T* | N = )*.

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269 305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of this result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair [A, B] of arbi