TY - JOUR

T1 - Strongly Irreducible Operators and Indecomposable Representations of Quivers on Infinite-Dimensional Hilbert Spaces

AU - Enomoto, Masatoshi

AU - Watatani, Yasuo

N1 - Publisher Copyright:
© 2015, Springer Basel.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00020-015-2228-3

DO - 10.1007/s00020-015-2228-3

M3 - Article

AN - SCOPUS:84949088984

SN - 0378-620X

VL - 83

SP - 563

EP - 587

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -