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Uday
Uday
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Are there any examples of non-Hilbert normed spaces which are isomorphic (in the norm sense) to their dual spaces? Or, is there any result in Functional Analysis which says that if a space is self-dual it has to be Hilbert space.

Since, we want isomorphism in the norm sense, examples like $\Re^{n}$$\mathbb{R}^{n}$ are ruled out. The norms of the space and its dual have to be equal and not just equivalent.

Thank you.

Are there any examples of non-Hilbert normed spaces which are isomorphic (in the norm sense) to their dual spaces? Or, is there any result in Functional Analysis which says that if a space is self-dual it has to be Hilbert space.

Since, we want isomorphism in the norm sense, examples like $\Re^{n}$ are ruled out. The norms of the space and its dual have to be equal and not just equivalent.

Thank you.

Are there any examples of non-Hilbert normed spaces which are isomorphic (in the norm sense) to their dual spaces? Or, is there any result in Functional Analysis which says that if a space is self-dual it has to be Hilbert space.

Since, we want isomorphism in the norm sense, examples like $\mathbb{R}^{n}$ are ruled out. The norms of the space and its dual have to be equal and not just equivalent.

Thank you.

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Uday
Uday
  • 2.2k
  • 22
  • 27

Self-dual normed spaces which are not Hilbert spaces

Are there any examples of non-Hilbert normed spaces which are isomorphic (in the norm sense) to their dual spaces? Or, is there any result in Functional Analysis which says that if a space is self-dual it has to be Hilbert space.

Since, we want isomorphism in the norm sense, examples like $\Re^{n}$ are ruled out. The norms of the space and its dual have to be equal and not just equivalent.

Thank you.