Active Oldest Votes. Many other references show when Googling "is a hilbert space if" banach. Improve this answer. Jochen Glueck 8, 2 2 gold badges 24 24 silver badges 44 44 bronze badges. Steve Huntsman Steve Huntsman Does anyone remember? Cheers to digital object identifiers! Add a comment. BigBill BigBill 1, 7 7 silver badges 14 14 bronze badges.
Garrisi Daniele Garrisi Daniele 1 1 silver badge 4 4 bronze badges. Rodriguez-Palacios] A Banach space is [isomorphic to] a Hilbert space iff it is uniformly homeomorphic to a Hilbert space.
Ady Ady 3, 1 1 gold badge 20 20 silver badges 31 31 bronze badges. Valerio Capraro Valerio Capraro 5, 1 1 gold badge 27 27 silver badges 47 47 bronze badges. Jonas Meyer Jonas Meyer 6, 2 2 gold badges 39 39 silver badges 49 49 bronze badges. Ralph: IMO it is reasonable to conjecture that there is no indecomposable space that is even just isomorphic to its dual.
Show 15 more comments. Active Oldest Votes. This raises two questions: Does there exist other centro-symmetric self dual convex polytopes? Improve this answer. Community Bot 1 2 2 silver badges 3 3 bronze badges. Denis Serre Denis Serre 45k 8 8 gold badges silver badges bronze badges. This remains a question, apparently open. Even if the unit ball is a polyhedron, which has to be centro-symmetric, why should it be regular?
So the Denis space is not isometric to a Hilbert space. It is, of course, linearly homeomorphic to a Hilbert space. The answer to my post also answers your questions about self-dual polytopes: there are centrally-symmetric self-dual polytopes in all dimensions. For instance, the supremum norm cannot be given by an inner product. Portions of this entry contributed by Mohammad Sal Moslehian. Portions of this entry contributed by Todd Rowland. Renteln, P. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.
Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Unlimited random practice problems and answers with built-in Step-by-step solutions.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search.
Can someone give me an example of a Banach space that is not a Hilbert space? I can't think of any because I don't know how to show one space that can not have inner product structure. We need to check that the parallelogram law is not satisfied. Linear functionals on such spaces can be written as an integral similar to the Hilbert space inner product but in general the functional cannot be associated with an element of the space itself. But there exists the notion of a semi-scalar product which was used by Lumer and Phillips in a study of contraction semi-groups see Yosida, Functional Analysis.
Sign up to join this community.
0コメント