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
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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