Metamath Proof Explorer


Table of Contents - 19.6.1. Operator sum, difference, and scalar multiplication

Note on operators. Unlike some authors, we use the term "operator" to mean any function from to . This is the definition of operator in [Hughes] p. 14, the definition of operator in [AkhiezerGlazman] p. 30, and the definition of operator in [Goldberg] p. 10. For Reed and Simon, an operator is linear (definition of operator in [ReedSimon] p. 2). For Halmos, an operator is bounded and linear (definition of operator in [Halmos] p. 35). For Kalmbach and Beran, an operator is continuous and linear (definition of operator in [Kalmbach] p. 353; definition of operator in [Beran] p. 99). Note that "bounded and linear" and "continuous and linear" are equivalent by lncnbd.

  1. df-hosum
  2. df-homul
  3. df-hodif
  4. df-hfsum
  5. df-hfmul
  6. hosmval
  7. hommval
  8. hodmval
  9. hfsmval
  10. hfmmval
  11. hosval
  12. homval
  13. hodval
  14. hfsval
  15. hfmval
  16. hoscl
  17. homcl
  18. hodcl