Strongly Irreducible Operators and Indecomposable Representations of Quivers on Infinite-Dimensional Hilbert Spaces

Masatoshi Enomoto, Yasuo Watatani

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1 Citation (Scopus)


We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are rephrased in terms of representations of quivers. We shall show two kinds of constructions of quite non-trivial indecomposable Hilbert representations (H, f) of the Kronecker quiver such that End(H, f) = CI which is called transitive. One is a perturbation of a weighted shift operator by a rank-one operator. The other one is a modification of an unbounded operator used by Harrison,Radjavi and Rosenthal to provide a transitive lattice.

Original languageEnglish
Pages (from-to)563-587
Number of pages25
JournalIntegral Equations and Operator Theory
Issue number4
Publication statusPublished - Dec 1 2015


All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory

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