An element (x1,…, xn) ∈ En is called a norming point of T ∈ L(nE) if ∥x1∥ = ⋯ = ∥xn∥ = 1 and ∣T(x1,…, xn)∣ = ∥T∥, where L(nE) denotes the space of all continuous n-linear forms on E. For T ∈ L(nE), we define Norm (T) = {(x1,…, xn) ∈ En: (x1,…, xn) is a norming point of T}. Norm (T) is called the norming set of T. We classify Norm (T) for every T ∈ L(2l2∞).
The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bilinear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
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