A reflexivity theorem for weakly closed subspaces of operators

A Reflexivity Theorem for Weakly Closed Subspaces of Operators

It was proved in [4] that the ultraweakly closed algebras generated by certain contractions on Hubert space have a remarkable property. This property, in conjunction with the fact that these algebras are isomorphic to Hx, was used in [3] to show that such ultraweakly closed algebras are reflexive. In the present paper we prove an analogous result that does not require isomorphism with Hx, and a...

Hyperinvariant subspaces and quasinilpotent operators

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

ε-weakly Chebyshev subspaces and quotient spaces

Invariant Subspaces and Hyper-reflexivity for Free Semigroup Algebras

In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very str...

A Bollobás-type theorem for affine subspaces