No Access
Chapter 6: Banach–Steinhaus
https://doi.org/10.1142/9789813232778_0006Cited by:0 (Source: Crossref)
Abstract:
As noted earlier there are two possible interpretations for the conclusion of the classical Uniform Boundedness Principle (UBP). If E is a Banach space, G is a normed space and Γ is a subset of the continuous linear operators from E into G which is pointwise bounded on E, then
(#) sup{‖Tx‖ : ‖x‖≤1,T∈Γ}=sup{‖T‖ :T∈Γ}<∞.
