Abstract
LetX denote a linear space of real valued functions defined on a subset of a Banach space such thatX containsE′ the dual space ofE as a subspace. Given a distinguished vectorx0 inE anx0-value (onX) is defined to be a projectionP fromX ontoE′ which satisfies the following two hypotheses: (VA) (PF)(x0)=Fx0 for allF inX; (VB) IfT is a continuous isomorphism fromE intoE such thatTx0=x0 thenP(F⋄T) = (PF) ⋄ T for allF inX. The existence and uniqueness of a value is established for two choices ofX, one of which is the space of polynomials in functional onE. The existence and partial uniqueness of a value is established on a third choice forX.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
