Note on invariant subspaces of a compact normal operator

@article{And1963NoteOI,
title={Note on invariant subspaces of a compact normal operator},
author={Tsuyoshi And{\^o}},
journal={Archiv der Mathematik},
year={1963},
volume={14},
pages={337-340}
}

An algebra of bounded operators on a Hilbert space H is said to be reductive if it is unital, weakly closed and has the property that if M ⊂ H is a (closed) subspace invariant for every operator in ,… Expand

We prove a theorem on the structure of weakly closed reductive operator algebras. The proof essentially relies on a known result of V. I. Lomonosov on transitive operator algebras containing a… Expand

A bounded linear operator A on a Hilbert space is called reductive if every invariant subspace of A reduces it. This paper gives examples of operators which give an affirmative answer to the… Expand

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… Expand

Theorem. If T is hyponormal, || Tn\\ =|| T\\n for all n. Proof. It is sufficient to prove that || A|[ =1 implies ||An|| =1 for all ». Consider the following property: (C„) For every e>0, there exists… Expand

Vector Spaces: 1. Complex vector spaces 2. First properties of vector spaces 3. Finite sums of vectors 4. Linear combinations of vectors 5. Linear subspaces, linear dependence 6. Linear independence… Expand