# Invariant subspaces for the family of operators which commute with a completely continuous operator

@article{Lomonosov1973InvariantSF,
title={Invariant subspaces for the family of operators which commute with a completely continuous operator},
author={Victor I. Lomonosov},
journal={Functional Analysis and Its Applications},
year={1973},
volume={7},
pages={213-214}
}
• V. Lomonosov
• Published 1973
• Mathematics
• Functional Analysis and Its Applications
132 Citations
Weakly invariant subspaces for multivalued linear operators on Banach spaces
Peter Saveliev generalized Lomonosov’s invariant subspace theorem to the case of linear relations. In particular, he proved that if S and T are linear relations defined on a Banach space X and havingExpand
A note on transitive localizing algebras
A simple proof is provided for a theorem of Troitsky that every nonzero quasinilpotent operator on a Banach space whose commutant is a localizing algebra has a nontrivial hyperinvariant subspace.
Invariant subspaces and Deddens algebras
It is shown that if the Deddens algebra ${\mathcal D}_T$ associated with a quasinilpotent operator $T$ on a complex Banach space is closed and localizing then $T$ has a nontrivial closedExpand
Some Open Problems and Conjectures Associated with the Invariant Subspace Problem
• Mathematics
• 2005
There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces and operators acting on complex Banach spaces. For instance, theExpand
On triangularization of algebras of operators.
• Mathematics
• 1981
A collection of operators on a fmite-dimensional space is said to be simultaneously triangularizable if there is a basis with respect to which all the operators have upper triangul r matrices. ThisExpand
11. On the Hypercyclicity Criterion for operators of Read’s type
Let $T$ be a so-called operator of Read's type on a (real or complex) separable Banach space, having no non-trivial invariant subset. We prove in this note that $T\oplus T$ is then hypercyclic, i.e.Expand
Operators on Banach spaces of Bourgain-Delbaen type
We begin by giving a detailed exposition of the original Bourgain-Delbaen construction and the generalised construction due to Argyros and Haydon. We show how these two constructions are related, andExpand
Strictly singular operators in Tsirelson like spaces
• Mathematics
• 2013
For each $n \in \mathbb{N}$ a Banach space $\mathfrak{X}_{0,1}^n$ is constructed is having the property that every normalized weakly null sequence generates either a $c_0$ or $\ell_1$ spreadingExpand
Remarks on Separation of Convex Sets, Fixed-Point Theorem, and Applications in Theory of Linear Operators
Some properties of the linear continuous operator and separation of convex subsets are investigated in this paper and a dual space for a subspace of a reflexive Banach space with a strictly convexExpand

#### References

SHOWING 1-3 OF 3 REFERENCES
Solution of an invariant subspace problem of K
• Mathematics, Physics
• 1966
An electronic regulating arrangement in which an analog signal generator is either inductively or capacitatively coupled with an electrically conductive element having an edge displaceable withExpand
INVARIANT SUBSPACES OF COMPLETELY CONTINOUS OPERATIONS
• Mathematics
• 1954
Abstract : A proof is presented of the theorem that if B is a Banach space and if T is a completely continuous operator in B, there then exist proper invariant subspaces of T. The proof assumesExpand