Strongly irreducible operators and indecomposable representations of quivers on infinite-dimensional Hilbert spaces

2013/03/11 by Masatoshi Enomoto, Enomoto, Masatoshi, Yasuo Watatani +1
Mathematics · #15A21 #16G20 #16G60 #47A15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47A65 #Secondary 46C07

paper · pdf · doi:10.48550/arxiv.1303.2485

openalex publication_date 2013/03/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

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 of the Kronecker quiver such that their endomorphism rings are trivial, which are 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.

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