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.