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 -