On The Uniqueness of The Strongly Irreducible Decompositions of Operators up to Similarity

Abstract

We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of direct integrals. Precisely, we study the uniqueness of strongly irreducible decompositions of the operators on the Hilbert spaces up to similarity.

17 pages

References in corpus (2)

• Direct integrals of strongly irreducible operators
• On a generalization of the Jordan canonical form theorem on separable Hilbert spaces