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Decomposition of an Algebra of Operators into Irreducible Algebras

In: Normed Algebras

Author

Listed:
  • M. A. Naimark

    (Academy of Sciences, Steklov Institute of Mathematics)

Abstract

A set S of bounded linear operators in the Hilbert space ℌ is said to be irreducible if there does not exist in ℌ a closed subspace, different from (0) and all of ℌ, which is invariant relative to all operators A ∈ S; otherwise, S is said to be reducible. In particular, a symmetric algebra R ⊂ $$\mathfrak{B}$$ (ℌ) is called irreducible or reducible if it is an irreducible or reducible set respectively.

Suggested Citation

  • M. A. Naimark, 1972. "Decomposition of an Algebra of Operators into Irreducible Algebras," Springer Books, in: Normed Algebras, chapter 0, pages 499-522, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-9260-3_8
    DOI: 10.1007/978-94-009-9260-3_8
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