8 citations · 19 across the 10 of their papers we have counts for
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Invariant subspace problem for rank-one perturbations: the quantitative version
Adi Tcaciuc
We show that for any bounded operator acting on infinite dimensional, complex Banach space, and for any , there exists an operator of rank at most one and no…
Isometries of combinatorial Banach spaces
C. Brech, V. Ferenczi, A. Tcaciuc
We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show…
On quasinilpotent operators and the invariant subspace problem
Adi Tcaciuc
We show that a bounded quasinilpotent operator acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator and…
The invariant subspace problem for rank one perturbations
Adi Tcaciuc
We show that for any bounded operator acting on an infinite dimensional Banach space there exists an operator of rank at most one such that has an invariant subspace…
Controlling almost-invariant halfspaces in both real and complex settings
Adi Tcaciuc, Ben Wallis
If is a bounded linear operator acting on an infinite-dimensional Banach space , we say that a closed subspace of of both infinite dimension and codimension is an al…
Every operator has almost-invariant subspaces
Alexey I. Popov, Adi Tcaciuc
We show that any bounded operator on a separable, reflexive, infinite-dimensional Banach space admits a rank one perturbation which has an invariant subspace of infinite di…