On the existence and uniqueness of complex structure and spaces with “few” operators
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- by Stanisław J. Szarek PDF
- Trans. Amer. Math. Soc. 293 (1986), 339-353 Request permission
Abstract:
We construct a $2n$-dimensional real normed space whose (Banach-Mazur) distance to the set of spaces admitting complex structure is of order ${n^{1/2}}$, and two complex $n$-dimensional normed spaces which are isometric as real spaces, but whose complex Banach-Mazur distance is of order $n$. Both orders of magnitude are the largest possible. We also construct finite-dimensional spaces with the property that all “well-bounded” operators on them are “rather small” (in the sense of some ideal norm) perturbations of multiples of identity. We also state some “metatheorem”, which can be used to produce spaces with various pathological properties.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 293 (1986), 339-353
- MSC: Primary 46B20; Secondary 47D15, 60D05
- DOI: https://doi.org/10.1090/S0002-9947-1986-0814926-5
- MathSciNet review: 814926