Kasyanov Pavlo O. - Qualitative and quantitative analysis of nonlinear systems: theory and applications
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- Book:Qualitative and quantitative analysis of nonlinear systems: theory and applications
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Existence and Regularity Results, Quantitative Methods and Their Convergence
and 
be real reflexive separable Banach spaces continuously embedded in a Hilbert space 
. Assume that 
we obtain the following tuples of continuous and dense embeddings: 
is the dual space to 
with respect to the pairing 
with the inner product 
on H .
, 
, 
For 
we consider the reflexive Banach space 
see section Special Classes of Bochner Integrable Functions. The Banach space 
with the norm 
is also reflexive (see section Special Classes of Bochner Integrable Functions). We identify the spaces 
and 
Similarly, 
. Let us define the duality form on 
, 
, 
.
such that 
, 
with continuous and dense embedding, 
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