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

  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},
  • V. Lomonosov
  • Published 1973
  • Mathematics
  • Functional Analysis and Its Applications
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 having
Invariant subspaces and Deddens algebras
Some Open Problems and Conjectures Associated with the Invariant Subspace Problem
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, the
On triangularization of algebras of operators.
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. This
11. On the Hypercyclicity Criterion for operators of Read’s type
  • S. Grivaux
  • Mathematics
    The Mathematical Legacy of Victor Lomonosov
  • 2020
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.
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, and
Strictly singular operators in Tsirelson like spaces
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 $\ell_1$ spreading
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 convex
Hyperinvariant subspaces for sets of polynomially compact operators
. We prove the existence of a non-trivial hyperinvariant subspace for several sets of polynomially compact operators. The main results of the paper are: (i) a non-trivial norm closed algebra A ⊆ B (


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 assumes
Solution of an invariant subspace problem of K
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 with