Grothendieck’s inequalities for JB$^*$-triples: Proof of the Barton–Friedman conjecture
| Autor: | Ondřej F. K. Kalenda, Antonio M. Peralta, Hermann Pfitzner, Jan Hamhalter |
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| Přispěvatelé: | Czech Technical University in Prague (CTU), Department of Mathematical Analysis, Charles University., Charles University [Prague] (CU), Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada (UGR), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO) |
| Rok vydání: | 2020 |
| Předmět: |
Conjecture
Applied Mathematics General Mathematics 010102 general mathematics Mathematics - Operator Algebras Hilbert space Cartesian product Bilinear form [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 16. Peace & justice 01 natural sciences Bounded operator Combinatorics symbols.namesake Bounded function FOS: Mathematics 46L70 17C65 symbols 0101 mathematics Operator Algebras (math.OA) Constant (mathematics) ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Transactions of the American Mathematical Society Transactions of the American Mathematical Society, American Mathematical Society, 2021, 374 (2), pp.1327-1350. ⟨10.1090/tran/8227⟩ |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/8227 |
| Popis: | We prove that, given a constant $K> 2$ and a bounded linear operator $T$ from a JB$^*$-triple $E$ into a complex Hilbert space $H$, there exists a norm-one functional $\psi\in E^*$ satisfying $$\|T(x)\| \leq K \, \|T\| \, \|x\|_{\psi},$$ for all $x\in E$. Applying this result we show that, given $G > 8 (1+2\sqrt{3})$ and a bounded bilinear form $V$ on the Cartesian product of two JB$^*$-triples $E$ and $B$, there exist norm-one functionals $\varphi\in E^{*}$ and $\psi\in B^{*}$ satisfying $$|V(x,y)| \leq G \ \|V\| \, \|x\|_{\varphi} \, \|y\|_{\psi}$$ for all $(x,y)\in E \times B$. These results prove a conjecture pursued during almost twenty years. Comment: 23 pages. We corrected a misprint, added some comments and precised one reference |
| Databáze: | OpenAIRE |
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