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}
}
  • T. Andô
  • Published 1 December 1963
  • Mathematics
  • Archiv der Mathematik
View on Springer
12 Citations
Background Citations
1
Methods Citations
1

12 Citations

Completely Reducible Operator Algebras and Spectral Synthesis
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 ,…
Non-self-adjoint operator algebras in Hilbert space
On Reductive Operators and Operator Algebras
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…
Invariant subspaces in the theory of operators and theory of functions
SOME CONDITIONS ON A REDUCTIVE OPERATOR IMPLYING NORMALITY OR SPECTRALITY
On transitive and reductive operator algebras
A note on reductive operators
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…
Operator algebras with reducing invariant subspaces.
Hyponormal operators and related topics
Completely reducible operators
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References

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INVARIANT SUBSPACES OF COMPLETELY CONTINOUS OPERATIONS
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…
On hyponormal operators
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…
Introduction to Hilbert Space
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…