20.500.12556/RUL-166410 Operators with a non-trivial closed invariant affine subspace We are concerned with the question of the existence of an invariant proper affine subspace for an operator $A$ on a complex Banach space. It turns out that the presence of the number $1$ in the spectrum of $A$ or in the spectrum of its adjoint operator $A^*$ is crucial. For instance, an algebraic operator has an invariant proper affine subspace if and only if $1$ is its eigenvalue. For an arbitrary operator $A$, we show that it has an invariant proper hyperplane if and only if $1$ is an eigenvalue of $A^*$. If $A$ is a power bounded operator, then every invariant proper affine subspace is contained in an invariant proper hyperplane, moreover, $A$ has a non-trivial invariant cone. invariant subspaces invariant affine subspaces power bounded operators invariantni podprostori invariantni afini podprostori potenčno omejeni operatorji true false true Angleški jezik Slovenski jezik Članek v reviji 2025-01-10 11:41:20 2025-01-10 11:41:23 2025-01-11 04:01:41 0000-00-00 00:00:00 2024 0 0 Str. 1305–1315 iss. 5 Vol. 98 Oct. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.9 0001-9054 10.1007/s00010-024-01090-0 221338371 s00010-024-01090-0.pdf s00010-024-01090-0.pdf 1 791C5A3AA7F401C9896772A1ADB6D698 1559d72f37463144e3547067272592d34b2aa7b755101ac1468f070bba90d295 f1e495d2-cf3e-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=198016 https://link.springer.com/article/10.1007/s00010-024-01090-0 1 b668dccb-cf3e-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=198015 Naravoslovnotehniška fakulteta 0 0 0